A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 10 inches in order to reduce the size of the paper to an area of 4 square inches. Find the width of the strip.
A) 5.0 in.
B) 3.5 in.
C) 4.0 in.
D) 4.5 in.

Question

Quizplus · Accepted Answer

Let x be the width of the strip to be cut off.

After the strip is cut off from all four sides, the new dimensions of the paper are (13-2x) inches by (10-2x) inches.

The new area of the paper is:

(13-2x)(10-2x) = 4

130 - 52x + 4x^2 = 4

4x^2 - 52x + 126 = 0

Dividing both sides by 2 gives:

2x^2 - 26x + 63 = 0

This equation factors as:

(2x - 9)(x - 7) = 0

The only positive solution is x = 4.5 inches.

Therefore, the width of the strip to be cut off is 4.5 inches.

A Strip of Uniform Width Is to Be Cut Off