A painting is 6 cm longer than it is wide. The painting is to be surrounded by a mat that is 2 cm wide and covered by a piece of glass with an area of 352cm squared. Find the dimensions of the painting. (A verbal model and equation is required)

Question

anonymous · Answer

L = W + 6   (1st sentence)
A = L * W


With the mat
L = W + 10    (2 cm more on each side)
W = W + 4     (2 cm more on each side)
Area of mat -  A = L* W
                       A = (W + 10)(W + 4)
                       A = W^2 + 4W + 10W + 40
                       A = W^2 + 14W + 40
352 = W^2 + 14W + 40
0 = W^2 + 14W - 312
0 = (W + 26)(W - 12)
W = -26 or W = 12
Can't use a negative width

W = 12
L = 18       (from first sentence L = W + 6)