Question

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?

Answer 1

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.

Answer 2

Answer: 33.33 %

step by step solution :-

If A = B × C, then if A is increased by R% then B is decreased by 100R/(100 + R)%.

Same, Area = Length×Breath

now because Length is increased by 50% then,

Breath should be decreased by

= 100×50/(100+50)

= 100 × 50 / 150

= 33.33 %