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
Algebra.Com
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): You can put this solution on YOUR website!
x, length
y, breadth
Original length,
Original area,
The described changes
Make a substitution for x, and solve for y....
then continue and finish.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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.
RELATED QUESTIONS
`The length of a rectangle is three times it’s breadth .If the breadth is decreased by... (answered by Theo)
the length of rectangle is increased by 2 cm. if length is increased by 4cm and breadth... (answered by CharlesG2)
Length of a rectangle is 5 cm less then twice its breadth, if the length is decreased by... (answered by ankor@dixie-net.com)
if the length of a rectangle is increased by 3cm and the breadth is 4cm, the area of the... (answered by josgarithmetic,MathTherapy)
If the length of the rectangle is exceeds its breadth by 7cm and the length is decreased... (answered by josgarithmetic)
The perimeter of a rectangular field is100m.if the length of the field is decreased by 2m (answered by macston)
The length of a rectangular plot of land exceeds its breadth by 23m.if the length is... (answered by Boreal)
the perimeter of rectangle 240 cm. its length is decreased by 10% & its breadth increased (answered by ankor@dixie-net.com)
Length of a rectangle is greater than its breadth by 3 CM if the length is increased by 9 (answered by josgarithmetic)