Chapter 9.4, Problem 46PPS

To determine

Find the new dimensions of the frame.

Answer to Problem 46PPS

Length is 80 inches and width is 6 inches.

Explanation of Solution

Given:

Before she begins painting a picture, Donna stretches her canvas over a wood frame. The frame has a length of 60 inches and a width of 4 inches. She has enough canvas to cover 480 square inches. Donna decided to increase the dimensions of the frame. The increase in length be 10 times the increase in width.

Concept Used:

Let $x$ = the increase in the width and let $10x$ = the increase in the length.

So $x+4$ is the new width and $10x+60$ is the new length.

Area: $A=l·w$

Calculation:

Let $x$ = the increase in the width and let $10x$ = the increase in the length.

So $x+4$ is the new width and $10x+60$ is the new length.

Area: $A=l·w$

The dimensions cannot be negative, so $x=2$ .

The width is $x+4=2+6=8$ inches and the length is $10x+60=10·2+60=20+60=80$ inches.

Thus, length is 80 inches and width is 6 inches.