SSAT Upper Level Quantitative - 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?

$3\sqrt{7}$

$7\sqrt{3}$

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 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:

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

$b=3\sqrt{7}$

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

$6\sqrt{2}$

$2\sqrt{6}$

$9\sqrt{6}$

$6\sqrt{9}$

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 from each side of the equation:

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

$b^{2}=121-49$

$b^{2}=72$

$b=\sqrt{72}$

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

$b=6\sqrt{2}$

Find the length of the missing side.

$4\sqrt{11}$

$8\sqrt2$

$4\sqrt{13}$

Explanation

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

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

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

$2\sqrt{34}$

$34\sqrt{2}$

$17\sqrt{2}$

$2\sqrt{17}$

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:

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

$36+100=c^{2}$

$136=c^{2}$

$\sqrt{136}=c$

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

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

$2\sqrt{34}=c$

Find the length of the missing side.

Explanation

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

$x=\sqrt{25}=5$

Find the length of the missing side.

Explanation

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

$x=\sqrt{64}=8$

Find the length of the missing side.

$10\sqrt3$

$10\sqrt5$

Explanation

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

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

Find the length of the missing side.

Explanation

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

$x=\sqrt{400}=20$

Find the length of the missing side.

Explanation

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

$x=\sqrt{1296}=36$

Find the length of the missing side.

Explanation

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

$x=\sqrt{225}=15$

How to find the length of the side of a right triangle

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation