SOLUTION: a rectangle has a perimeter of 38 centimeters and a area of 84 centimeters.what are the dimension of the rectangle

Question 291941: a rectangle has a perimeter of 38 centimeters and a area of 84 centimeters.what are the dimension of the rectangle
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
P = 2(L+W) = 38 cm
A = L*W = 84 cm^2
L = 84/W
2(84/W+W)=38
Divide both sides by 2.
84/W + W = 19
Multiply through by W to remove denominator.
84 + W^2 = 19W
Subtract 19W from both sides.
W^2 - 19W + 84 = 0
Factor.
(W-7)(W-12) = 0
So,
W = 7 or W = 12
It is a rectangle, which means logically, if
W = 7, then L = 12
and if
W = 12, then L = 7.
Checking the perimeter...
2(7+12) = 38??
2(19) = 38
Correct.
.
Answer
L = 7 and W = 12
or
L = 12 and W = 7
.
Done
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