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High School Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

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Example Questions

Example Question #31 : Triangles

A park is designed to fit within the confines of a triangular lot in the middle of a city. The side that borders Elm street is 15 feet long. The side that borders Broad street is 23 feet long. Elm street and Broad street meet at a right angle. The third side of the park borders Popeye street, what is the length of the side of the park that borders Popeye street?

Possible Answers:

16.05 feet

22.5 feet

18.5 feet

27.46 feet

17.44 feet

Correct answer:

27.46 feet

Explanation:

This question requires the use of Pythagorean Theorem. We are given the length of two sides of a triangle and asked to find the third. We are told that the two sides we are given meet at a right angle, this means that the missing side is the hypotenuse. So we use a²+ b²= c², plugging in the two known lengths for a and b. This yields an answer of 27.46 feet.

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Example Question #32 : Right Triangles

A right triangle has legs of 15m and 20m. What is the length of the hypotenuse?

Possible Answers:

30m

35m

25m

40m

45m

Correct answer:

25m

Explanation:

The Pythagorean theorem is a² + b² = c², where a and b are legs of the right triangle, and c is the hypotenuse.

(15)² + (20)² = c² so c² = 625. Take the square root to get c = 25m

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Example Question #34 : Triangles

Paul leaves his home and jogs 3 miles due north and 4 miles due west. If Paul could walk a straight line from his current position back to his house, how far, in miles, is Paul from home?

Possible Answers:

√14

Correct answer:

Explanation:

By using the Pythagorean Theorem, we can solve for the distance “as the crow flies” from Paul to his home:

3² + 4² = x²

9 + 16 = x²

25 = x²

5 = x

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Example Question #92 : Plane Geometry

Given a right triangle where the two legs have lengths of 3 and 4 respectively, what is the length of the hypotenuse?

Possible Answers:

Correct answer:

Explanation:

The hypotenuse can be found using Pythagorean Theorem, which is a²+ b²= c², so we plug in a = 3 and b = 4 to get c.

c²=25, so c = 5

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Example Question #31 : Triangles

Triangle

Length AB = 4

Length BC = 3

If a similar triangle has a hypotenuse length of 25, what are the lengths of its two legs?

Possible Answers:

5 and 25

20 and 25

15 and 25

3 and 4

15 and 20

Correct answer:

15 and 20

Explanation:

Similar triangles are in proportion.

Use Pythagorean Theorem to solve for AC:

Pythagorean Theorem: AB² + BC² = AC²

4² + 3² = AC²

16 + 9 = AC²

25 = AC²

AC = 5

If the similar triangle's hypotenuse is 25, then the proportion of the sides is AC/25 or 5/25 or 1/5.

Two legs then are 5 times longer than AB or BC:

5 * (AB) = 5 * (4) = 20

5 * (BC) = 5 * (3) = 15

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Example Question #31 : 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 #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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

Possible Answers:

$10\ in$

$20\ in$

$12\ in$

$14\ in$

$7\ in$

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 #61 : Geometry

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:

1/2 inches

1 inches

4.5 inches

4 inches

6 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 #162 : Plane Geometry

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:

185 inches

13.6 inches

184 inches

14.2 inches

13.7 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 #163 : Plane Geometry

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

10.1 feet

10.6 feet

10.5 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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High School Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #31 : Triangles

Example Question #32 : Right Triangles

Example Question #34 : Triangles

Example Question #92 : Plane Geometry

Example Question #31 : Triangles

Example Question #31 : Right Triangles

Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #61 : Geometry

Example Question #162 : Plane Geometry

Example Question #163 : Plane Geometry

All High School Math Resources

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