If the length of a rectangle is increased by 50
Asked by admin @ in Math viewed by 340 People
The length of a rectangle is increased by 50 percent. By what percent would the width have to be decreased to maintain the same area?
Answered by admin @
Let the length of the rectangle be x cm and the breadth of the rectangle = y cm
Therefore
area of the rectangle = x * y = xy cm²
Now,
The length is increased by 50%
Therefore
length = x + 50% of x
= x + 50/100 *x
= x + x/2
= 3x/2
Given that area is constant
Therefore
xy = 3x/2 * breadth
breadth = 2xy/3x = 2y/3 cm
Percentage of increase in breadth = decrease in breadth/original breadth *100
= (y - 2y/3)/y * 100
= ((3y - 2y) / 3)/y*100
= y/3y *100
= 100/3
= 33.333%
The breadth is decreased by 33.333% to maintain the same area.
Hope this helps you.
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