Question 362684
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 = {{{48/4}}}
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