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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 3: Q. 3.78 (page 362)

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.

Short Answer

Expert verified

The length of the hypotenuse is 13.

Step by step solution

01

Step 1. Given information.

A right triangle is given with the length of two of its legs as $12, 5$ .

We need to find the length of the hypotenuse, c.

02

Step 2. Use Pythagorean Theorem.

By Pythagorean theorem,

$c^{2} = a^{2} + b^{2} c = \sqrt{a^{2} + b^{2}}$

03

Step 3. Substitute values in the Pythagorean theorem.

We get

$c = \sqrt{12^{2} + 5^{2}} = \sqrt{144 + 25} = \sqrt{169}$

Use the definition of square root.

$c = 13$

So the length of the hypotenuse is 13.

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