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ACT Math : Kites

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Example Questions

Example Question #4 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $\displaystyle 18$ . The perimeter of the kite is $\displaystyle 88$ . Find the length of the sum of the remaining two sides.

Possible Answers:

$\displaystyle 42$

$\displaystyle 52$

$\displaystyle 22$

$\displaystyle 26$

$\displaystyle 44$

Correct answer:

$\displaystyle 52$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

To find the sum of the remaining two sides:

$\displaystyle 88=18+18+2(side)$ $\displaystyle 188=40+40+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 88=36+2(side)$

$\displaystyle 2(side)=88-36=52$

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Example Question #1 : How To Find The Length Of The Side Of A Kite

Kite vt act

The kite shown above has two adjacent sides both with a measurement of $\displaystyle 12$ . The perimeter of the kite is $\displaystyle 38$ . Find the sum of the remaining two sides.

Possible Answers:

$\displaystyle 14$

14.5 $\displaystyle 14.5$

7.5 $\displaystyle 7.5$

$\displaystyle 7$

$\displaystyle 19$

Correct answer:

$\displaystyle 14$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. This problem also provides the perimeter measurement of the kite. Therefore, use the information that is provided to find the difference between the perimeter and the sum of the congruent adjacent sides provided in the question.

To find the sum of the remaining two sides:

$\displaystyle 38=12+12+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 38=24+2(side)$

$\displaystyle 2(side)=38-24=14$

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Example Question #6 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $15\textup{ inches}$ $\displaystyle 15\textup{ inches}$ . The perimeter of the kite is $55\textup{ inches}$ $\displaystyle 55\textup{ inches}$ . Find the length of one of the remaining two sides.

Possible Answers:

$12.5\textup{ inches}$ $\displaystyle 12.5\textup{ inches}$

$15\textup{ inches}$ $\displaystyle 15\textup{ inches}$

$7.5\textup{ inches}$ $\displaystyle 7.5\textup{ inches}$

$25\textup{ inches}$ $\displaystyle 25\textup{ inches}$

$30\textup{ inches}$ $\displaystyle 30\textup{ inches}$

Correct answer:

$12.5\textup{ inches}$ $\displaystyle 12.5\textup{ inches}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

$\displaystyle 55=15+15+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 55=30+2(sides)$

$\displaystyle 2(sides)=55-30 = 25$

$side=\frac{25}{2}=12.5$ $\displaystyle side=\frac{25}{2}=12.5$

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Example Question #7 : How To Find The Length Of The Side Of A Kite

Kite vt act

Using the kite shown above, find the length of side $\displaystyle x$ .

Possible Answers:

$4\textup{ ft}$ $\displaystyle 4\textup{ ft}$

$4.5\textup{ ft}$ $\displaystyle 4.5\textup{ ft}$

$1.5\textup{ ft}$ $\displaystyle 1.5\textup{ ft}$

$2\textup{ ft}$ $\displaystyle 2\textup{ ft}$

$2.5\textup{ ft}$ $\displaystyle 2.5\textup{ ft}$

Correct answer:

$2\textup{ ft}$ $\displaystyle 2\textup{ ft}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

The solution is:

$\displaystyle 13=4.5+4.5+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 13=9+2(sides)$

$\displaystyle 2(sides)=13-9 = 4$
Since the remaining two sides have a total length of $\displaystyle 4$ ft, side $\displaystyle x$ must be $\frac{4}{2}=2$ $\displaystyle \frac{4}{2}=2$

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Example Question #8 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $35\textup{ mm}$ $\displaystyle 35\textup{ mm}$ . The perimeter of the kite is $90\textup{ mm}$ $\displaystyle 90\textup{ mm}$ . Find the length of one of the remaining two sides.

Possible Answers:

$20\textup{mm}$ $\displaystyle 20\textup{mm}$

$5\textup{mm}$ $\displaystyle 5\textup{mm}$

$\sqrt{10}\textup{mm}$ $\displaystyle \sqrt{10}\textup{mm}$

$10\textup{mm}$ $\displaystyle 10\textup{mm}$

$15\textup{mm}$ $\displaystyle 15\textup{mm}$

Correct answer:

$10\textup{mm}$ $\displaystyle 10\textup{mm}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

$\displaystyle 90=35+35+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 90=70+2(sides)$

$\displaystyle 2(sides)=90-70 = 20$

$side=\frac{20}{2}=10$ $\displaystyle side=\frac{20}{2}=10$

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Example Question #9 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $40\textup{mm}$ $\displaystyle 40\textup{mm}$ . The perimeter of the kite is $188\textup{mm}$ $\displaystyle 188\textup{mm}$ . Find the length of the sum of the remaining two sides.

Possible Answers:

$148\textup{mm}$ $\displaystyle 148\textup{mm}$

$108\textup{mm}$ $\displaystyle 108\textup{mm}$

$112\textup{mm}$ $\displaystyle 112\textup{mm}$

$59\textup{mm}$ $\displaystyle 59\textup{mm}$

$54\textup{mm}$ $\displaystyle 54\textup{mm}$

Correct answer:

$108\textup{mm}$ $\displaystyle 108\textup{mm}$

Explanation:

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Example Question #1 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $55\textup{mm}$ $\displaystyle 55\textup{mm}$ . The perimeter of the kite is $200\textup{mm}$ $\displaystyle 200\textup{mm}$ . Find the length of one of the remaining two sides.

Possible Answers:

$52.5\textup{mm}$ $\displaystyle 52.5\textup{mm}$

$110\textup{mm}$ $\displaystyle 110\textup{mm}$

$90\textup{mm}$ $\displaystyle 90\textup{mm}$

$45\textup{mm}$ $\displaystyle 45\textup{mm}$

$55\textup{mm}$ $\displaystyle 55\textup{mm}$

Correct answer:

$45\textup{mm}$ $\displaystyle 45\textup{mm}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

$\displaystyle 200=55+55+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 200=110+2(sides)$

$\displaystyle 2(sides)=200-110 = 90$

$side=\frac{90}{2}=45$ $\displaystyle side=\frac{90}{2}=45$

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Example Question #31 : Kites

A kite has two adjacent sides both with a measurement of 11.5 $\displaystyle 11.5$ . The perimeter of the kite is $\displaystyle 45$ . Find the length of the sum of the remaining two sides.

Possible Answers:

11.75 $\displaystyle 11.75$

$\displaystyle 23$

$\displaystyle 21$

22.5 $\displaystyle 22.5$

$\displaystyle 22$

Correct answer:

$\displaystyle 22$

Explanation:

This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

The solution is:

$\displaystyle 45=11.5+11.5+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 45=23+2(sides)$

$\displaystyle 2(sides)=45-23 = 22$

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Example Question #31 : Quadrilaterals

A kite has two adjacent sides both with a measurement of $\frac{3}{4}\textup{mm}$ $\displaystyle \frac{3}{4}\textup{mm}$ . The perimeter of the kite is $28\textup{ inches}$ $\displaystyle 28\textup{ inches}$ . Find the length of one of the remaining two sides.

Possible Answers:

$\frac{5}{12}\textup{ inch}$

$3.5\textup{ inches}$ $\displaystyle 3.5\textup{ inches}$

$5\textup{ inches}$ $\displaystyle 5\textup{ inches}$

$10\textup{ inches}$ $\displaystyle 10\textup{ inches}$

$\frac{10}{12}\textup{ft}$ $\displaystyle \frac{10}{12}\textup{ft}$

Correct answer:

$5\textup{ inches}$ $\displaystyle 5\textup{ inches}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

$\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}=9 in.$ $\displaystyle \frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}=9 in.$

The solution is:

$\displaystyle 28=9+9+2(side)$ , where side= $\displaystyle side=$ one of the two missing sides.

$\displaystyle 28=18+2(sides)$

$\displaystyle 2(sides)=28-18 = 10$

$side=\frac{10}{2}=5$ $\displaystyle side=\frac{10}{2}=5$

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Example Question #1 : How To Find The Perimeter Of Kite

A kite has two shorter sides and two longer sides. Each of the shorter sides has a length of 19 and each of the longer sides has a length of 25. What is the perimeter of the kite?

Possible Answers:

$\displaystyle 76$

$\displaystyle 88$

100 $\displaystyle 100$

$\displaystyle 94$

Correct answer:

$\displaystyle 88$

Explanation:

Remember that a kite has two adjacent sets of shorter sides as well as two adjacent sets of longer sides.

Use the formula for perimeter of a kite:

$P=2s_{1}+2s_{2}$ $\displaystyle P=2s_{1}+2s_{2}$

Where $\displaystyle P$ is the perimeter, s_1 $\displaystyle s_1$ is the length of the shorter sides, and s_2 $\displaystyle s_2$ is the length of the longer sides.

$P=(2\times 19)+(2\times 25)=88$ $\displaystyle P=(2\times 19)+(2\times 25)=88$

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ACT Math : Kites

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Find The Length Of The Side Of A Kite

Example Question #1 : How To Find The Length Of The Side Of A Kite

Example Question #6 : How To Find The Length Of The Side Of A Kite

Example Question #7 : How To Find The Length Of The Side Of A Kite

Example Question #8 : How To Find The Length Of The Side Of A Kite

Example Question #9 : How To Find The Length Of The Side Of A Kite

Example Question #1 : How To Find The Length Of The Side Of A Kite

Example Question #31 : Kites

Example Question #31 : Quadrilaterals

Example Question #1 : How To Find The Perimeter Of Kite

All ACT Math Resources

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