Chapter 8.1, Problem 37E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# Given: The area of right △ A B C (not shown) is 40  in 2 . m ∠ C = 90 ∘ A C = x B C = x + 2 Find: x

To determine

To find:

The value of x.

Explanation

Solving for the value of the x is follow by the formulae,

Area of the right triangle A=12abÂ unit2

Where a and b are the sides of the triangle.

Calculation:

Given,

Area of right â–³ABCÂ A=40Â in2

AC=x

BC=x+2, and

mâˆ c=900

Area of the right triangle A=12abÂ unit2

Where, a=AC=x

b=BC=x+2

A=12ab

40=12(x)(x+2)

Multiply by 2 on both sides,

2(40)=2(12)(x)(x+2)

80=(x)(x+2)

By distributive property of multiplication

80=xâ‹…x+xâ‹…2

80=x2+2x

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