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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #42 : Right Triangles

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 #484 : Geometry

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:

3 and 4

5 and 25

15 and 25

15 and 20

20 and 25

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 #481 : Psat Mathematics

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 #33 : Right Triangles

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

Possible Answers:

$12\ in$

$7\ in$

$20\ in$

$14\ in$

$10\ in$

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 #486 : 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

6 inches

4 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 #482 : Psat Mathematics

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

13.7 inches

14.2 inches

13.6 inches

184 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 #55 : 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:

10.6 feet

10.8 feet

10.5 feet

10.2 feet

10.1 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 #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Righttriangle

Given:

A = 2 miles

B = 3 miles

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

Possible Answers:

3.5 miles

3.4 miles

3.7 miles

3.2 miles

3.6 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 #491 : Geometry

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:

9.4 feet

8.6 feet

18 feet

3.6 feet

6.4 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 #492 : Geometry

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

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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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #42 : Right Triangles

Example Question #484 : Geometry

Example Question #481 : Psat Mathematics

Example Question #33 : Right Triangles

Example Question #486 : Geometry

Example Question #482 : Psat Mathematics

Example Question #55 : Triangles

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

Example Question #491 : Geometry

Example Question #492 : Geometry

All High School Math Resources

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