SOLUTION: Draw one rectangle that has both a perimeter of 18 centimeters and an area of 18 square centimeters. Label the width and length

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Question 130076: Draw one rectangle that has both a perimeter of 18 centimeters and an area of 18 square centimeters. Label the width and length
Found 2 solutions by checkley71, Earlsdon:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
x*y=18 or x=18/y
2x+2y=18 now replace x by (18/y) & solve for y:
2(18/y)+2y=18
36/y+2y=18
(36+2y^2)/y=18 now cross multiply
36+2y^2=18y
2y^2-18y+36=0
2(y^2-9y+18)=0
2(y-6)(y-3)=0
y-6=0
y=6 answer
y-3=0
y=3 answer.
so the sides of this rectangle are 3 & 6 cm.
proof:
3*6=18
2*(18/6)+2*3=18
36/6+6=18
12+6=18
18=18

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with:
A+=+L%2AW Substitute A = 18.
1) 18+=+L%2AW and...
P+=+2L%2B2W Substitute P = 18.
2) 18+=+2L%2B2W Simplify to: 9+=+L%2BW
Rewrite equation 2) as:L+=+9-W and substitute into equation 1) then solve for W.
18+=+%289-W%29%2AW
18+=+9W-W%5E2 Rearrange to:
W%5E2-9W%2B18+=+0 Factor.
%28W-3%29%28W-6%29+=+0
W+=+3 or W+=+6
Use the smaller value for W, so W = 3 and L = 9-W = 6
The solution:
The length is 6cm. and the width is 3cm.