SOLUTION: The length of a rectangle is 4 cm less than 3 times its width. If the lenght is increased by 8 cm and the width is decreased by 2 cm, the perimeter will be 100 cm. Find the dimensi

Question 62096: The length of a rectangle is 4 cm less than 3 times its width. If the lenght is increased by 8 cm and the width is decreased by 2 cm, the perimeter will be 100 cm. Find the dimensions of the original rectangle.
Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 4 cm less than 3 times its width. If the lenght is increased by 8 cm and the width is decreased by 2 cm, the perimeter will be 100 cm. Find the dimensions of the original rectangle.
Let W be the width of the original rectangle.
Let L be the length of the original rectangle. Then, .
If the perimeter becomes 100 when L is increased by 8 and when W is decreased by 2 then:
Old perimeter = .
New perimeter = .
We use the fact that to replace L in the new perimeter equation with .
So, .
Or, .
Or, .
Or, .
Or, .
So, .
.
So, .
Verify:
If L is increased by 8 and W is decreased by 2 then and . So, the perimeter is .
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