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ACT Math : Geometry

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Example Questions

Example Question #61 : Right Triangles

If the base of a right triangle is 5 cm long and the height of the triangle is 7 cm longer than the base, what is the length of the third side of the triangle in cm?

Possible Answers:

Correct answer:

Explanation:

Find the height of the triangle 5 + 7 = 12

Use the Pythagorean Theorem to solve for the length of the third side, or hypotenuse.

$c^{2} = a^{2} + b^{2}$

$c^{2} = 5^{2} + 12^{2}$

$c^{2} = 25 + 144 = 169$

c = 13

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Example Question #44 : Right Triangles

Given the right triangle in the diagram, what is the length of the hypotenuse?

Possible Answers:

$7\ in$

$10\ in$

$12\ in$

$20\ in$

$14\ in$

Correct answer:

$10\ in$

Explanation:

To find the length of the hypotenuse use the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

Where and are the legs of the triangle, and is the hypotenuse.

$6^{2}+8^{2}=100$

$(100)^{\frac{1}2}=10$

The hypotenuse is 10 inches long.

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Example Question #45 : Right Triangles

Righttriangle

Triangle ABC is a right triangle. If the length of side A = 3 inches and C = 5 inches, what is the length of side B?

Possible Answers:

4 inches

6 inches

1 inches

1/2 inches

4.5 inches

Correct answer:

4 inches

Explanation:

Using the Pythagorean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This gives:

$3^{2} + b^{2} = 5^{2}$

$9 + b^{2} = 25$

Subtracting 9 from both sides of the equation gives:

$b^{2} = 16$

b = 4 inches

Righttriangle

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Example Question #52 : Right Triangles

Righttriangle

Triangle ABC is a right triangle. If the length of side A = 8 inches and B = 11 inches, find the length of the hypoteneuse (to the nearest tenth).

Possible Answers:

13.6 inches

14.2 inches

184 inches

13.7 inches

185 inches

Correct answer:

13.6 inches

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$8^{2} + 11^{2} = C^{2}$

$64 + 121 = C^{2}$

$185 = C^{2}$

Taking the square root of both sides, we find that C = 13.6 inches

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Example Question #43 : Triangles

Righttriangle

Given:

A = 6 feet

B = 9 feet

What is the length of the hypoteneuse of the triangle (to the nearest tenth)?

Possible Answers:

10.2 feet

10.8 feet

10.5 feet

10.1 feet

10.6 feet

Correct answer:

10.8 feet

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$6^{2} + 9^{2} = C^{2}$

$36 + 81 = C^{2}$

$117 = C^{2}$

Taking the square root of both sides, we find that C = 10.8

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Example Question #61 : Right Triangles

Righttriangle

Given:

A = 2 miles

B = 3 miles

What is the length of the hypoteneuse of triangle ABC, to the nearest tenth?

Possible Answers:

3.6 miles

3.5 miles

3.4 miles

3.7 miles

3.2 miles

Correct answer:

3.6 miles

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$2^{2} + 3^{2} = C^{2}$

$4 + 9 = C^{2}$

$13 = C^{2}$

Taking the square root of both sides, we find that C = 3.6

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Example Question #53 : Right Triangles

Given that two sides of a right triangle measure 2 feet and 3 feet, respectively, with a hypoteneuse of x, what is the perimeter of this right triangle (to the nearest tenth)?

Possible Answers:

3.6 feet

9.4 feet

8.6 feet

6.4 feet

18 feet

Correct answer:

8.6 feet

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$2^{2} + 3^{2} = C^{2}$

$4 + 9 = C^{2}$

$13 = C^{2}$

Taking the square root of both sides, we find that C = 3.6

To find the perimeter, we add the side lengths together, which gives us that the perimeter is: 3 + 2 + 3.6 = 8.6

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Example Question #54 : Right Triangles

$In\;\Delta GHJ, \;what\;is\;the\;length\;of\;\overline{GJ}?$

Possible Answers:

Correct answer:

Explanation:

$Use\;the\;Pythagorean\;Theorem:A^2+B^2=C^2,\;to\; find\;\overline{GJ}.$

5^2+12^2=C^2

25+144=C^2

169=C^2

$C=\sqrt{169}=13$

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Example Question #62 : Right Triangles

Kathy and Jill are travelling from their home to the same destination. Kathy travels due east and then after travelling 6 miles turns and travels 8 miles due north. Jill travels directly from her home to the destination. How miles does Jill travel?

Possible Answers:

$\dpi{100} \small 12\ miles$

$\dpi{100} \small 8\ miles$

$\dpi{100} \small 10\ miles$

$\dpi{100} \small 16\ miles$

$\dpi{100} \small 14\ miles$

Correct answer:

$\dpi{100} \small 10\ miles$

Explanation:

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

$\dpi{100} \small 6^{2}+8^{2}=x^{2}$

$\dpi{100} \small 36+64=x^{2}$

$\dpi{100} \small x=10$ miles

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Example Question #71 : Geometry

$Which\; of \;the \;following \;is\; NOT\; true\; about \;the \;hypotenuse \;of \;a\; triangle?$

Possible Answers:

$It\;is\;always\;across\;from\;the\;largest\;angle\;in\;the\;triangle.$

$It\;is\;across\;from\;the\;right\;angle.$

$It\;is\;the\;longest\;side.$

$It\;is\;always\;greater\;than\;1.$

Correct answer:

$It\;is\;always\;greater\;than\;1.$

Explanation:

$The\;hypotenuse\;can\;be\;between\;0\;and\;1.$

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ACT Math : Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #61 : Right Triangles

Example Question #44 : Right Triangles

Example Question #45 : Right Triangles

Example Question #52 : Right Triangles

Example Question #43 : Triangles

Example Question #61 : Right Triangles

Example Question #53 : Right Triangles

Example Question #54 : Right Triangles

Example Question #62 : Right Triangles

Example Question #71 : Geometry

All ACT Math Resources

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