SOLUTION: Hi, Here is my question from the first chapter of an Algebra I text. The section is on the distributive property and even though the question is about area and perimeter I know t

Question 483840: Hi,
Here is my question from the first chapter of an Algebra I text. The section is on the distributive property and even though the question is about area and perimeter I know that the book wants me to use the distributive property to solve it.
"What are the length and width of a rectangle if the area is 13.5 square units and the length of one side is 1/5 the measure of the perimeter?"
I have tried everything including drawing it out on graph paper. I was able to get very close to the right answer by taking the square root of 13.5 Then I multiplied that by 4 to find the perimeter of the square. Then I multiplied that by four to find the perimeter (which I know to be 15 because the answer is in the back of the book). Then I multiplied the perimeter by 1/5 to find the length of one side, then I could subtract to find the other side. My answers were close to the answers in the book but they were still off by fractions. I need to know how to set up and solve the equation using the distributive property!
Thank you! -Joe
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Area = 13.5
Length = 13.5 / W
length = 1/5 perimeter
Perimeter = 2(L+W)
13.5/W = 2/5(L+W)
5*13.5/W = 2((13.5/W)+W)
multiply by W
5*13.5 = 2(13.5+w^2)
67.5= 27+2W^2
67.5-27=2W^2
40.5= 2W^2
W^2=40.5/2
W=4.5
L= 13.5/4.5
L= 3
CHECK
Perimeter = 2(3+4.5)= 15
1/5 of 15 = 3 the length
Area = 3*4.5=13.5 unit^2
m.ananth@hotmail.com
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