SOLUTION: The expression 2(l+ w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13 1/2 square units and the length of one side

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: The expression 2(l+ w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13 1/2 square units and the length of one side       Log On


   

Question 94377This question is from textbook Algebra 1
: The expression 2(l+ w) may be used to find the perimeter of a rectangle. What are the length and width 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? This question is from textbook Algebra 1

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The expression 2(l+ w) may be used to find the perimeter of a rectangle. What are the length and width 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?
:
Using decimal for 1/5. L = .2 * perimeter:
L = .2(2(L+W))
L = .4(L+W)
L = .4L + .4W
1L - .4L = .4W
.6L = .4W
:
Area is given as 13.5 sq units
L * W = 13.5
W = 13.5/L
:
Substitute (13.5/L) for W in the .6L = .4W equation
.6L = .413.5%2FL
.6L = 5.4%2FL
Multiply equation by L
.6L%5E2 = 5.4
:
Divide both sides by .6
L%5E2 = 5.4%2F.6
:
L%5E2 = 9
L = sqrt%289%29
L = 3
:
Find W:
W = 13.5/3
W = 4.5 units
:
Perimeter = 2(3) + 2(4.5) = 15
Length/Perimeter: 3/15 = 1/5