SOLUTION: Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 86 feet. Suppose that the width of a rectangle is three fee

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Question 662834: Suppose that the width of a rectangle is three feet shorter than length and that the
perimeter of the rectangle is 86 feet.
Suppose that the width of a rectangle is three feet shorter than length and that the
perimeter of the rectangle is 86 feet.
a) Set up an equation for the perimeter involving only L, the length of the rectangle.
Answer:
b) Solve this linear equation algebraically to find the length of the rectangle. Find
the width as well.
Answer: Length ______, Width ______
Show your work here:
c) Using the same width from your answer on part b), find a new perimeter when
the new length is five less than three times the width.
Answer:
Explain your work here in one or two sentences:

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 86+ft.

a) Set up an equation for the perimeter involving only L, the length of the rectangle.
Answer:
P=2L%2B2W....given that W=L-3ft
P=2L%2B2%28L-3ft%29

P=2L%2B2L-6ft
P=4L-6ft

b) Solve this linear equation algebraically to find the length of the rectangle. Find the width as well.

Answer: Length is 23ft, Width is 20ft
Show your work here:
P=4L-6ft......plug in P=86+ft
86+ft=4L-6ft
86+ft%2B6ft=4L
92ft=4L
92ft%2F4=L
23ft=L
W=L-3ft..plug in L
W=23ft-3ft
W=20ft

c) Using the same width from your answer on part b), find a new perimeter when the new length is five+less than three times the width.
Answer: W=20ft L=3W-5ft...=>...L=3%2A20ft-5ft=>...L=60ft-5ft=>...L=55ft
P=2%2A55ft%2B2%2A20ft
P=110ft%2B40ft
P=150ft
Explain your work here in one or two sentences: you do this part