SOLUTION: A rectangular ceiling tile has a perimeter of 134 inches and an area of 1,102 square inches. What are the dimensions of the tile?

Question 938590: A rectangular ceiling tile has a perimeter of 134 inches and an area of 1,102 square inches. What are the dimensions of the tile?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Area = length x width = 1102 in^2
Perimeter = L + W + L + W = 2L + 2W = 134 in
= 2(L+W)= 134 in
So:
L+W=67 in and LxW=1102 in^2
Solve the first equation for L:
(L+W)-W=67-W
L=67-W
Substitute in the other equation and solve for W:
(67-W)x W= 1102 in^2
67W - W^2= 1102 in^2...................Add w^2 to both sides
67W-W^2+(W^2)= 1102 in^2 + (w^2)...........Subtract 67W from both sides
67W-67W= 1102 in^2 + W^2 - 67W.......Re-arrange right side
0= W^2 - 67W + 1102
0= (W-38)(W-29)
Thus we have W-38=0 and w-29=0
so length is 38 and width is 29
Check:
area = L x W=38 in x 29 in =1102 in^2, the given
perimeter = 2(38 in)+ 2(29 in)=76 + 58= 134 in, also given
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