Question

You are constructing a metal border of uniform width for a rectangular wall mirror that measures 20 inches by 24 inches. You have 416 square inches of metal to use. What is the greatest possible width * of the border

Answer 1

The frame will be 4 inches in width

Explanation:

The length of the outside is 24+2x

The width of the outside is 20+2x

(24+2x)(20+2x) - 20(24) = 416

480 + 40x + 48x + 4x2 - 480 = 416

4x2 + 88x - 416 = 0

x2 + 22x - 104 = 0

(x+26)(x-4) = 0

x = -26 or x=4

The frame will be 4 inches in width