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The perimeter of a rectangle is 32m and the area of the rectangle is 60 m2 Find the dimensions of the rectangle?
Perimeter, P = 32 m
Area, A = 60 m^2.
A = LW
60= LW
L = 60/W
P = 2L + 2W
32= 2L + 2W substitute 60/W for L;
32= 2(60/W) + 2W divide by 2 to both sides;
16 = 60/W + W multiply by W to both sides;
16W = 60 + W^2
0 = 60 + W^2 - 16W or,
W^2 - 16W + 60 = 0
W = [16 +,- square root of [16^2 - (4)(1)(60)]/2
W = [16 +,- square root of (256 -240)]/2
W = (16 +,- square root of 16)/2
W = (16 + 4)/2 or W = (16 - 4)/2
W = 20/2 or W = 12/2
W = 10 m or W = 6 m
L = 60/W = 60/10 or L = 60/6
L = 6 m or L = 10 m
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