SOLUTION: The width is a rectangle is three fourths of the length. the perimeter of the rectangle becomes 50cm when the length and the width are each increased by 2cm. Find the length and th

Algebra ->  Rectangles -> SOLUTION: The width is a rectangle is three fourths of the length. the perimeter of the rectangle becomes 50cm when the length and the width are each increased by 2cm. Find the length and th      Log On


   

Question 795293: The width is a rectangle is three fourths of the length. the perimeter of the rectangle becomes 50cm when the length and the width are each increased by 2cm. Find the length and the width.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let W = original width
Let L = original length
:
Write an equation for each statement:
:
"The width is a rectangle is three fourths of the length."
W = .75L
:
" the perimeter of the rectangle becomes 50cm when the length and the width are each increased by 2cm.
2(L+2) + 2(W+2) = 50
Simplify, divide by 2
L + 2 + W + 2 = 25
L + W + 4 = 25
L + W = 25 - 4
L + W = 21
Replace W with .75L
L + .75L = 21
1.75L = 21
L = 21/1.75
L = 12 cm is the length
then obviously
.75(12) = 9 cm is the width
;
:
Check this in the statement:
"the perimeter of the rectangle becomes 50cm when the length and the width are each increased by 2cm."
2(14) + 2(11) = 50