SOLUTION: A rectangular cement patio has an area of 80 square meters. Its perimeter is 36 meters. What are the dimensions of the patio?

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Question 957639: A rectangular cement patio has an area of 80 square meters. Its perimeter is 36 meters. What are the dimensions of the patio?

Found 2 solutions by josgarithmetic, macston:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
L, length
w, width
A, area
p, perimeter
-
Constants, A=80, p=36.
Unknowns, w, L.

FORMULAS:
p=2w+2L, A=wL


The formulas themselves are two equations in two unknown variables. Solve the system for w and L.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular cement patio has an area of 80 square meters. Its perimeter is 36 meters. What are the dimensions of the patio?
L=length; W=width; P=perimeter=36m; A=area=80sqm
P=2(L+W)
36m=2(L+W) Divide each side by 2.
18m=L+W Subtract W from each side
18m-W=L
A=L%2AW Substitute for L.
A=%2818m-W%29%28W%29
A=18Wm-W%5E2 Plug in value for A.
80m%5E2=18Wm-W%5E2 Subtract 80m^2 from each side.
0=-x%5E2%2B18Wm-80m%5E2 Multiply each side by -1.
0=x%5E2-18W%2B80
0=%28W-8%29%28W-10%29
W=8m or W=10m ANSWER 1: Width is 8 meters.(or 10m)
18m-W=L
18m-8m=L
10m=L ANSWER 2: Length is 10 meters. (or 8m)