Question

If the length of a rectangle is decreased by 20%, what should be the increase in the breadth of the rectangle so that the area remains the same?

Answer 1

Let x and y represent the length and breadth of the rectangle respectively.

∴ The original area of the rectangle = xy

There is a 20% decrease in length.

∴ New length = `"x" - 20/100 "x" = "x" - 1/5 "x"`

= `"x"(1 - 1/5) = "x"((5 - 1)/5) = 4/5 "x"`

Let k% be the required increase in breadth

∴ New breath = `"y" + "k"/100 "y"`

= `"y"(1 + "k"/100)`

Given that the new and old areas should be equal.

∴ `(4/5"x")(1 + "k"/100)"y"` = xy

∴ `(4/5)((100 + "k")/100) = 1`

∴ `(100 + "k")/100 = 5/4`

∴ 100 + k = 125

∴ k = 125 - 100 = 25

Breadth should be increased by 25% so that the area remains same.