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Intermediate Geometry : Plane Geometry

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Example Questions

Example Question #1 : How To Find If Kites Are Similar

Suppose the ratio of a kite's side lengths is $\sqrt 2$ to $\sqrt3$ . Find a similar kite.

Possible Answers:

$\sqrt6:1$

$1:\sqrt6$

$\sqrt7:\sqrt6$

$\sqrt6:\sqrt{54}$

$\sqrt6:3$

Correct answer:

$\sqrt6:3$

Explanation:

To find a similar kite, first take the ratios of the two sides and convert this to fractional form.

$\sqrt2:\sqrt3= \frac{\sqrt2}{\sqrt3}$

Rationalize the denominator.

$\frac{\sqrt2}{\sqrt3}=\frac{\sqrt2}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}=\frac{\sqrt6}{3}$

The ratios of $\sqrt2:\sqrt3$ matches that of $\sqrt6:3$ .

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Example Question #2 : How To Find If Kites Are Similar

Suppose a kite has side lengths of and . What must the side lengths be for a similar kite?

Possible Answers:

1,2

6,10

5,9

12,15

2,3

Correct answer:

12,15

Explanation:

Write the side lengths 4 and 5 as a ratio.

4:5

The only side lengths that match this ratio by a scale factor of is 12:15 .

$4\cdot 3:5\cdot 3 \rightarrow 12:15$

Therefore, the correct side lengths are 12,15 .

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Example Question #1 : Kites

If a kite has lengths of and , what is the perimeter?

Possible Answers:

$6\sqrt2$

$9\sqrt2$

Correct answer:

Explanation:

Write the formula to find the perimeter of a kite.

P=2(a+b)

Substitute the lengths and solve.

P=2(2+4)=12

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Example Question #1 : Kites

If a kite has lengths of $\frac{1}{4}$ and $\frac{1}{2}$ , what is the perimeter?

Possible Answers:

$\frac{1}{8}$

$\frac{3}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{6}{7}$

Correct answer:

$\frac{3}{2}$

Explanation:

Write the formula for the perimeter of a kite.

P=2(a+b)

Substitute the lengths and solve.

$P=2\left(\frac{1}{4}+\frac{1}{2}\right) = 2\left(\frac{1}{4}+\frac{2}{4}\right)=2\left(\frac{3}{4}\right)=\frac{3}{2}$

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Example Question #1 : Kites

What is the perimeter of a kite if the lengths were and y^2 ?

Possible Answers:

$\sqrt2 xy^2$

2x+2y^2

4x^2+2y^4

2x+y^2

$\frac{xy^2}{2}$

Correct answer:

2x+2y^2

Explanation:

Write the formula to find the perimeter of a kite.

P=2(a+b)

Substitute the lengths and simplify.

P=2(x+y^2)=2x+2y^2

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

The diagonals of a kite are inches and inches respectively. Two of the sides of the kite are each inches. Find the length of the other two sides.

Possible Answers:

15 in.

12 in.

13 in.

16 in.

20 in.

Correct answer:

15 in.

Explanation:

We would do best to begin with a picture.

One of our diagonals is bisected by the other, and thus each half is 12. The other important thing to recall is that the diagonals of a kite are perpendicular. Therefore we have four right triangles. We can then use the Pythagorean Theorem to calculate the upper portion of the vertical diagonal to be 5. That means that the bottom portion of our diagonal is 9.

Using the Pythagorean Theorem, we can calculate our remaining sides to be 15.

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

A kite has a perimeter of inches. One pair of adjacent sides of the kite have a length of inches. What is the measurement for each of the other two sides of the kite?

Possible Answers:

$\frac{6}{5}in$

7in

6in

$\frac{7}{2}in$

20in

Correct answer:

7in

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

26=2(6+b)

$\frac{26}{2}=(6+b)$

13=6+b

b=13-6=7

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Example Question #4 : Kites

A kite has a perimeter of mm. One pair of adjacent sides of the kite have lengths of mm. What is the measurement for one of the other two sides of the kite?

Possible Answers:

14mm

6mm

13mm

8mm

24mm

Correct answer:

13mm

Explanation:

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Example Question #2 : How To Find The Length Of The Side Of A Kite

A kite has a perimeter of inches. One pair of adjacent sides of the kite have lengths of inches. What is the measurement for one of the other two sides of the kite?

Possible Answers:

4in

3in

7in

1in

$\frac{7}{2}in$

Correct answer:

3in

Explanation:

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Example Question #311 : Plane Geometry

Vt_custom_kite_series_int._geo

Using the kite shown above, find the length of side

Possible Answers:

18cm

11cm

21cm

9cm

$\frac{21}{2}cm$

Correct answer:

18cm

Explanation:

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find If Kites Are Similar

Example Question #2 : How To Find If Kites Are Similar

Example Question #1 : Kites

Example Question #1 : Kites

Example Question #1 : Kites

Example Question #1 : 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 #4 : Kites

Example Question #2 : How To Find The Length Of The Side Of A Kite

Example Question #311 : Plane Geometry

All Intermediate Geometry Resources

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