SOLUTION: a rectangle is three times as long as it is wide. the rectangle has its length increased in the ratio of 3:1 and its width decreases in the ratio 1:2. a. in what ratio is its area

Question 703880: a rectangle is three times as long as it is wide. the rectangle has its length increased in the ratio of 3:1 and its width decreases in the ratio 1:2.
a. in what ratio is its area changed?
b. in what ratio is its perimeter changed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a rectangle is three times as long as it is wide.
L = 3W
the rectangle has its length increased in the ratio of 3:1 and its width decreases in the ratio 1:2.
3L by .5W
:
a. in what ratio is its area changed?
Old area:new area
LW:3L*.5W
LW:1.5LW
get rid of the decimal mult both by 2
2LW:3LW
divide both by LW
2:3 is the ratio of old area to new area
:
b. in what ratio is its perimeter changed?
(2L+2W):(2*3L+.5*2W)
2(L+W):(6L+1W)
Replace L with 3W
2(3W+W):(18W+W)
2(4W):19W
8W:19W
8:19 is the old perimeter to the new perimeter
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