Dimensions- Mirror

[Guest]

A rectangular mirror is placed in a frame 4 inches wide.

Area of mirror- 972 square inches.

Area of frame- 568 square inches.

Calculate length and width of the mirror.

[Guest]

For the frame.....
Let L = length of overall frame
Let W = width of mirror inside frame

8L + 8W = 568
So L + W = 71 ........ L = (71 - W)

For mirror....
W(L - = 972
WL - 8W = 972
W(71-W) - 8W = 972
Gives W^2 - 63W + 972 = 0
This factorises.... (W - 36)(W - 27) = 0
So W = 36 or 27
Width of mirror is 27, Length of mirror is 36
Length with frame is 36 + 8 = 44
width with frame is 27 + 8 = 35