SOLUTION: What are the length (l) and width (w) of a rectangle if the area is 13-1/2 square units and the length of one side is 1/5 the measure of the perimeter? Explain your reasoning.

Question 97268This question is from textbook Algebra 1
: What are the length (l) and width (w) of a rectangle if the area is 13-1/2 square units and the length of one side is 1/5 the measure of the perimeter? Explain your reasoning.
8th grader needs some help & mom hasn't had an advanced math class in nearly 30 years. Any help would be appreciated. This question is from textbook Algebra 1

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What are the length (l) and width (w) of a rectangle if the area is 13-1/2 square units and the length of one side is 1/5 the measure of the perimeter? Explain your reasoning.
-------------
Let width be x units and length be y units:
Area = xy = 27/2 sq. units
--------------
Perimeter = 2x + 2y
EQUATION:
x = (1/5)(2x+2y)
x = (2/5)x + (2/5)y
(3/5)x = (2/5)y
3x = 2y
y = (3/2)x
-----------------------
Re-writing the equations:
xy = (27/2)
y = (3/2)x
----------------
Substitute to solve for x:
x[(3/2)x] = (27/2)
(3/2)x^2 = (27/2)
x^2 = 9
x = 3
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Substitue into xy = (27/2) to solve for y:
3y = 27/2
y = 9/2
=============
Checking:
xy = (27/2) ?
3(9/2) = 27/2
27/2 = 27/2
==============
Cheers,
Stan H.

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