Question

A rectangular picture frame is

5
inches wide and
12
inches tall. You want to make the area
5
times as large by increasing the length and width by the same amount.
Find the number of inches by which each dimension must be increased. Round to the nearest tenth.

Answer 1

Explanation:

The current area is 60 sq. in. You wish to increase this area to 300 sq. in. by adding x in two dimensions: namely length and width.

These measurements would be 5 + x wide and 12 + x long.

(5 + x)(12 + x) = 300

x^2 + 17x + 60 = 300

Subtracting 300 from both sides and using the quadratic formula for

x^2 + 17x - 240 = 0,

we find that the one reasonable answer for the measure x is 9.2 inches.