The outside of a mosaic frame measures 14 in by 20 in., and 160 in^2 of mirror shows. Find the width of the frame.

Question

The outside of a mosaic frame measures 14 in by 20 in., and 160 in^2 of mirror shows. Find the width of the frame.

Answer 1

Let X = width of the frame.  The frame is on all 4 sides of the mirror (top and bottom, left and right) so the area of the mirror is 

 

(14 - 2*X)*(20 - 2*X) = 160

280 - 40*X - 28*X + 4*X^2 = 160

4*X^2 - 68*X + 120 = 0

X - 17*X + 30 = 0

(X - 15)*(X - 2) = 0

X -15 = 0  or  X - 2 = 0

X = 15  or X = 2

 

X = 15 will result in a negative mirror size so choose X = 2 in as the width of the frame 

 

Check:  (14 - 4)*(20 - 4) = 10*16 = 160 in^2 mirror