SOLUTION: A rectangle has a width 4cm less than the length. If a new rectangle is formed by increasing the width 5cm and decreasing the length 3cm, the area of this resulting rectangle is 11

Question 801159: A rectangle has a width 4cm less than the length. If a new rectangle is formed by increasing the width 5cm and decreasing the length 3cm, the area of this resulting rectangle is 117cm^2. What are the dimensions of the original rectangle? I'm not entirely sure how to approach this problem.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rectangle has a width 4cm less than the length.
Length = L
Width = L-4
========================
If a new rectangle is formed by increasing the width 5cm and decreasing the length 3cm, the area of this resulting rectangle is 117cm^2.
Length = L-3
Width = L-4+5 = L+1
========================
Equation:
Area = length * width
117 = (L-3)(L+1)
L^2 -2L -3 = 117
L^2 -2L - 120 = 0
--
Factor:
(L-12)(L+10) = 0
Positive solution:
L = 12 cm (original length)
---
W = L-4 = 8 cm (original width)
What are the dimensions of the original rectangle?
========================
Cheers,
Stan H.
========================
RELATED QUESTIONS
a rectangle has a length that is 1m less than twice its width. increasing the width by 3m (answered by ankor@dixie-net.com)

The length of a rectangle is 8cm longer than the width. If the width is increased by 4cm... (answered by ikleyn)

The length of a rectangle is three less than twice its width. If the length is increased... (answered by ankor@dixie-net.com)

: The width of a rectangle is 5cm less than its length. If its perimeter is 38cm, find... (answered by ReadingBoosters)

A given rectangle has a length 2 feet longer than it's width. If the width is shortened... (answered by josgarithmetic)

the length of a rectangle is 5cm less than twice its width . if the length is decreased... (answered by macston)

find the perimeter of a rectangle whose length is 5cm less than twice its... (answered by mananth)

Suppose the width of a rectangle is 5cm less than half its length. Its area is 72 cm... (answered by JBarnum)

The width of a rectangle is 5cm less than half its length. Its area is 72cm^2. What is... (answered by nerdybill,sigma10)