The length of a rectangle is increased by 50%, by what percent would the width have to be decreased to maintain sane area?

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 as the length is increased by 50% ∴ length = x + 50% of x                   = x + 50/100 *x                   = x + x/2                   = 3x/2 Given that area is constant so, 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% (Ans)