Answer:
√22 -2.5 ≈ 2.19 inches
Step-by-step explanation:
If x represents the width of the frame, then the dimensions of the framed picture are (4+2x) by (6+2x). The area of the frame is the difference between the area of the framed picture and the area of the picture:
frame area = 63 in^2 = (4+2x)·(6+2x) - 4·6 = 4x^2 +20x
Dividing by 4, we have ...
x^2 + 5x = 63/4
Completing the square gives ...
x^2 +5x + 6.25 = 22
(x +2.5)^2 = 22
x + 2.5 = √22
x = √22 -2.5 ≈ 2.19 . . . . . inches
The width of the frame is about 2.19 inches. (Exactly √22 -2.5 inches.)
