   Chapter 8.1, Problem 38E 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 lengths of the legs of a right triangle are consecutive even integers. The numerical value of the area is three times that of the longer leg. Find the lengths of the legs of the triangle.

To determine

To find:

The lengths of the legs of the triangle.

Explanation

Finding the lengths of the legs of the right triangle is follow by the formulae,

Area of the right triangle A=12(ab) unit2

Where a and b are the sides of the triangle.

Calculation:

Given,

The length of the legs of a right triangle are consecutive even integers. The numerical value of the area is three times that of the longer leg.

Let x and x+2 are the length of the two legs of a right triangle.

Here,

x+2 is the longer leg.

Area of the triangle (A) is 3 times of that longer leg.

(i.e.) A=3(x+2)

Area of the right triangle A=12(ab) unit2

Where, a=x and b=x+2

A=12(x)(x+2)

Since, A=3(x+2)

3(x+2)=12(x)(x+2)

Divide by (

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