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SSAT Upper Level Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #2 : Properties Of Triangles

A right triangle has a hypotenuse of 39 and one leg is 36. What is the length of the other leg?

Possible Answers:

Correct answer:

Explanation:

You may recognize these numbers as multiples of 13 and 12 (each by a factor of 3) and remember that sides of length 5, 12 and 13 make a special right triangle. So the other leg would be 15 $(5\times 3)$ .

If you don't remember this, you can use Pythagorean theorem:

$39^{2}-36^{2}= 1521-1296=225$

$\sqrt{225}=15$

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

A right triangle has a hypotenuse of and one leg has a length of . What is the length of the other leg?

Possible Answers:

$3\sqrt{7}$

$7\sqrt{3}$

Correct answer:

$3\sqrt{7}$

Explanation:

When calculating the lengths of sides of a right triangle, we can use the Pythagorean Theorem as follows:

$a^{2}+b^{2}=c^{2}$ , where and are legs of the triangle and is the hypotenuse.

Plugging in our given values:

$9^{2}+b^{2}=12^{2}$

Subtracting 9^2 from each side of the equation:

$b^{2}=12^{2}-9^{2}$

$b^{2}=144-81$

$b^{2}=63$

Taking the square root of each side of the equation:

$b=\sqrt{63}$

Simplifying the square root:

$b=\sqrt{9\times 7}$

$b=3\sqrt{7}$

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

A right triangle has two legs of length and , respectively. What is the hypotenuse of the right triangle?

Possible Answers:

$34\sqrt{2}$

$17\sqrt{2}$

$2\sqrt{34}$

$2\sqrt{17}$

Correct answer:

$2\sqrt{34}$

Explanation:

When calculating the lengths of sides of a right triangle, we can use the Pythagorean Theorem as follows:

$a^{2}+b^{2}=c^{2}$ , where and are legs of the triangle and is the hypotenuse.

Plugging in our given values:

$6^{2}+10^{2}=c^{2}$

$36+100=c^{2}$

$136=c^{2}$

$\sqrt{136}=c$

$\sqrt{17\times 8}=c$

$\sqrt{17\times 4\times 2}=c$

$2\sqrt{34}=c$

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

A right triangle has a leg of length and a hypotenuse of length . What is the length of the other leg?

Possible Answers:

$9\sqrt{6}$

$2\sqrt{6}$

$6\sqrt{2}$

$6\sqrt{9}$

Correct answer:

$6\sqrt{2}$

Explanation:

When calculating the lengths of sides of a right triangle, we can use the Pythagorean Theorem as follows:

$a^{2}+b^{2}=c^{2}$ , where and are legs of the triangle and is the hypotenuse.

Plugging in our given values:

$7^{2}+b^{2}=11^{2}$

Subtracting 7^2 from each side of the equation:

$b^{2}=11^{2}-7^{2}$

$b^{2}=121-49$

$b^{2}=72$

$b=\sqrt{72}$

$b=\sqrt{36\times 2}$

$b=6\sqrt{2}$

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Example Question #11 : Properties Of Triangles

Find the length of the missing side.

Possible Answers:

160

$4\sqrt{10}$

$\sqrt{15}$

Correct answer:

$4\sqrt{10}$

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

x^2+6^2=14^2

x^2+36=196

x^2=160

$x=\sqrt{160}=4\sqrt{10}$

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Example Question #12 : Properties Of Triangles

Find the length of the missing side.

Possible Answers:

$4\sqrt{11}$

176

$8\sqrt2$

$4\sqrt{13}$

Correct answer:

$4\sqrt{11}$

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

x^2+7^2=15^2

x^2+49=225

x^2=176

$x=\sqrt{176}=4\sqrt{11}$

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Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

x^2+12^2=13^2

x^2+144=169

x^2=25

$x=\sqrt{25}=5$

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Example Question #13 : Properties Of Triangles

Find the length of the missing side.

Possible Answers:

100

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

x^2+24^2=26^2

x^2+576=676

x^2=100

$x=\sqrt{100}=10$

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Example Question #14 : Properties Of Triangles

Find the length of the missing side.

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

x^2+6^2=10^2

x^2+36=100

x^2=64

$x=\sqrt{64}=8$

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

Find the length of the missing side.

Possible Answers:

300

$10\sqrt5$

$10\sqrt3$

Correct answer:

$10\sqrt3$

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

x^2+10^2=20^2

x^2+100=400

x^2=300

$x=\sqrt{300}=10\sqrt{3}$

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SSAT Upper Level Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #2 : Properties Of Triangles

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

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

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

Example Question #11 : Properties Of Triangles

Example Question #12 : Properties Of Triangles

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Example Question #13 : Properties Of Triangles

Example Question #14 : Properties Of Triangles

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

All SSAT Upper Level Math Resources

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