SOLUTION: Solve, Show your work to help me understand. The length of a rectangle is 3 times the width. if the length is increased by 4cm and the width is decreased by 1cm, the perimeter w

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Question 362684: Solve, Show your work to help me understand.
The length of a rectangle is 3 times the width. if the length is increased by 4cm and the width is decreased by 1cm, the perimeter will be 102cm. Find the dimensions of the origional rectangle.
Answer by ankor@dixie-net.com(22740) (Show Source):
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The length of a rectangle is 3 times the width.
if the length is increased by 4cm and the width is decreased by 1cm,
the perimeter will be 102cm.
Find the dimensions of the original rectangle.
:
Let x = the width of the original rectangle
It says, "length of a rectangle is 3 times the width."; so we have;
3x = the length of the original rectangle
then
(3x + 4) = length of the new rectangle
and
(x-1) = width of the new rectangle
:
Perimeter of the new rectangle:
2(3x+4) + 2(x-1) = 102
Simplify, divide by 2 and we have:
3x + 4 + x - 1 = 51
4x + 3 = 51
4x = 51 - 3
4x = 48
x =
x = 12 cm is the original width
then
3(12) = 36 cm is the original length
:
:
Check the perimeter with these values
2(36+4) + 2(12-1) =
2(40) + 2(11) = 102, confirms our solutions