   Chapter 5.4, Problem 23E 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

A rectangle has base length x+3, altitude length x+1, and diagonals of length 2x each. What are the lengths of its base, altitude, and diagonals?

To determine

To Find:

Lengths of the base, altitude and diagonals of the rectangle.

Explanation

Given A right triangle has legs of lengths x and 2x+2 and a hypotenuse of length 2x+3.

The figure can be redrawn as,

From the given data,

Length of the base = x+3.

Length of the altitude = x+1.

Length of the diagonal = 2x.

From the figure,

ABC is a right triangle,

AC is a hypotenuse and AB and BC are the legs of the triangle.

From the Pythagorean Theorem,

AC2=AB2+BC2(2x)2=(x+3)2+(x+1)24x2=x2+6x+9+x2+2x+14x2=2x2+8x+104x

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