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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 206 (page 145)

Use the Pythagorean Theorem to find the length of the hypotenuse.

Short Answer

Expert verified

The length of the hypotenuse is 13.

Step by step solution

01

Given information:

From the given righttriangle, we have:

the lengths of the legs: $a = 12$ and $b = 5$ .

Let the length of hypotenuse be $" c "$ .

02

Step 2:

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

03

Step 3:

Substitute the given values in the formula,

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

04

Step 4:

On simplifying:

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

05

Step 5:

Take square root on both sides,

$\sqrt{c^{2}} = \sqrt{169} = \sqrt{{(13)}^{2}} c = 13$

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