Question
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 ?
Answers
Steve
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
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