SOLUTION: The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle?

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Question 348138: The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle?
Let x = width
and y = length
.
From:"The area of a rectangle is 30 square centimeters" (equation 1)
xy = 30
.
From: "perimeter is 26 centimeters" (equation 2)
26=2(x+y)
.
Solve equation 2 for y:
26=2(x+y)
13=x+y
13-x = y
.
Substitute above into equation 1 and solve for x:
xy = 30
x(13-x) = 30
13x-x^2 = 30
0 = x^2-13x+30
0 = (x-15)(x+2)
x = {-2, 15}
We can toss out the negative solution leaving
x = 15 centimeters
.
Substitute above into equation 1 and solve for y:
xy = 30
15y = 30
y = 2 centimeters
.
Dimensions of rectangle:
2 by 15 centimeters