The frame around a rectangular picture has a uniform width. The dimensions of the picture are 5 in. by 7 in. If the combined area of the picture and the frame is 80 in.2, what is the width of the frame?
+91 First, find the area of the picture:
5*7 = 35 in2
The area of just the frame is:
80 - 35 = 45 in2
Now, note that the frame is nothing but 4 equal squares for the corners of the frame and 4 rectangles.
The corners have an area of x2.
Two of the rectangles have an area of 5x, and the other 2 have an area of 7x.
Therefore the area of the frame is
4(x2) + 2(5x) + 2(7x) = 4x2 + 24x
Which equals:
4x2 + 24x = 45
Solving the quadratic, we get:
4x2 + 24x = 45
4x2 + 24x - 45 = 0
(2x-3)(2x+15) = 0
2x - 3 = 0
2x = 3
x = 1.5
(The other solution for x would be negative)
Therefore, the width is 1.5 in2.
Solved! :)
