Question

A portrait has dimensions of 50 inches by 60 inches and is surrounded by a frame of uniform width. If the total area (portrait plus frame) is 3456 square inches, find the width of the frame

Answer 1

2 inches

Explanation:

If x is the width of the frame, then the overall dimensions are ...

(50 +2x) by (60 +2x)

so the area is ...

3456 = (50 +2x)(60+2x)

x^2 +55x -114 = 0 . . . . . . . divide by 4, subtract the left side

(x +57)(x -2) = 0 . . . . . . . . . factor

Solutions to this are x=2 and x=57 (extraneous).

The width of the frame is 2 inches.