SOLUTION: The length of a rectangle is three times it’s breadth .If the breadth is decreased by by 2m and the length increased by 4m,the area of rectangle is decreased by athird .Find the
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Question 1151633: The length of a rectangle is three times it’s breadth .If the breadth is decreased by by 2m and the length increased by 4m,the area of rectangle is decreased by athird .Find the breadth of original rectangle.Hence finds its area. Found 2 solutions by josgarithmetic, jim_thompson5910:Answer by josgarithmetic(39617) (Show Source):
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x = original length = 3y
y = original breadth or width
A = original area = length*width = x*y = 3y*y = 3y^2
width decreases by 2 ---> y becomes y-2
length increases by ---> x becomes x+4
area is now equal to (new length)*(new width) = (x+4)(y-2)
the old area was 3y^2. One-third of this is y^2 (simply divide by 3), so when it decreases by one-third then we have 3y^2-y^2 = 2y^2 of an area. Basically we have 2/3 of the original area.
(x+4)(y-2) = 2y^2
(3y+4)(y-2) = 2y^2 .... plug in x = 3y
3y(y-2)+4(y-2) = 2y^2 .... distributive rule
3y^2-6y+4y-8 = 2y^2 .... distributive rule
3y^2-2y-8 = 2y^2
3y^2-2y-8-2y^2 = 0
y^2-2y-8 = 0
(y-4)(y+2) = 0 .... factor
y-4 = 0 or y+2 = 0 .... zero product property
y = 4 or y = -2
A negative width does not make sense, so we toss out y = -2 and only focus on y = 4
The original width is 4 meters
Now find the original length
x = 3y
x = 3*4
x = 12
The original length and width of the rectangle is 12 by 4, giving an original area of 12*4 = 48
One-third of this is 48/3 = 16, so if the area decreases by one-third then we have 48-16 = 32 as the new area (note how 32/48 = 2/3). Or you could take 2/3 of 48 and get 32. Either way the new area is 32 square meters.
If we increase the length by 4 and decrease the width by 2, then we have
old length = 12 ----> new length = 16
old width = 4 ---> new width = 2
new area = (new length)*(new width) = 16*2 = 32
which matches up with the previous 32 we got. This helps confirm the answer.
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