Apic measuring 4*6 in is placed inside a frame which has equal width around entire picture. if the area of frame around picture is 63 square inches, what is width of frame?

√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.)

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step-by-step explanation: