   Chapter 8.2, Problem 32E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

The perimeter of a right triangle is 12 m. If the hypotenuse has a length of 5 m, find the lengths of the two legs.

To determine

To Find:

The lengths of the two legs of a right triangle provided its perimeter and hypotenuse.

Explanation

Formula Used:

Pythagorean theorem for the right angle triangle ABC for the hypotenuse AC,

AC2=AB2+BC2.

The perimeter of a polygon is the sum of the lengths of all sides of the polygon. That is, P=a+b+c, where a,b and c are the side lengths of the triangle.

Calculation:

It is given that the perimeter of a right triangle is 12 m and its hypotenuse length is 5 m.

Let the two legs are a and b.

Then the hypotenuse must be c=5 m.

Substituting the value of 'c' in the perimeter formula,

a+b+5=12

a+b=7

b=7-a➝(1)

Applying the Pythagorean Theorem for the sides of the triangle,

a2+b2=c2

a2+b2=52

a2+b2=25

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