SOLUTION: The length of a rectangle is twice its width. If the length is decreased by 10ft. and the width is increased by 8ft., the area is increased by 100 sq.ft. What are the dimension of

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is twice its width. If the length is decreased by 10ft. and the width is increased by 8ft., the area is increased by 100 sq.ft. What are the dimension of       Log On


   

Question 895123: The length of a rectangle is twice its width. If the length is decreased by 10ft. and the width is increased by 8ft., the area is increased by 100 sq.ft. What are the dimension of the rectangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w and L.
L=2w
A=wL
-
Changes to w and L.
L-10 for length
w+8 for width
A%2B100=%28w%2B8%29%28L-10%29

Substitute for A.
wL%2B100=%28w%2B8%29%28L-10%29
Begin simplifying.
wL%2B100=wL%2B8L-10w-80
100=8L-10w-80
180=8L-10w
50=4L-5w

We were given a description for how L and w are related; so substitute for L.
4L-5w=50
4%2A2w-5w=50
3w=50
w=50%2F3
highlight%28w=16%262%2F3%29
L=2%2816%262%2F3%29
L=32%2B4%2F3
highlight%28L=33%261%2F3%29