Question

A painting with dimensions 10 inches by 14 inches is placed in a picture frame (of constant width), increasing its area to 221 square inches. How many inches is the width of the picture frame?

Answer 1

Answer:

1.5 inches

Step-by-step explanation:

(10+2x)(14+2x) = 221

4x² + 48x - 81 = 0

4x² + 54x - 6x - 81 = 0

2x(2x + 27) - 3(2x + 27) = 0

(2x + 27)(2x - 3) = 0

x = -27/2, 3/2

x = 3/2 or 1½ or 1.5 inches