The area of a frame is equal to 120in^2.it surrounds a 4in x 6in photo.the frame is of uniform width.how wide is the frame ?

Answer 1

the 4x6 photo has area 24 in^2
So, the frame has area 120-24 = 96 in^2

If the frame has width x, then its area is

2(4x) along the ends
+2(6x) along the sides
+4x^2 on the corners

so,

4x^2 + 8x + 12x = 96
x^2 + 5x - 24 = 0
x = 3

So, the frame is 3in wide

check:
total dimensions are 10x12, so area = 120