Question

The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units the area is increased by 67 square units if length is increased by 3 units and breadth is increased by 2 units. Find the perimeter of the rectangle.

Answer 1

HEY FRIEND,

YOUR ANSWER :

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

Then, area of rectangle = xy

Now,

Case I ==> (x-5)(y+3) = xy - 9
==> xy + 3x - 5y - 15 = xy - 9
==> 3x - 5y = 6 -----(i)

Case II ==> (x+3)(y+2) = xy + 67
==> xy + 2x + 3y + 6 = xy + 67
==> 2x + 3y = 61 -----(ii)

Multiplying (i) & (ii) by 2 & 3 respectively,

==> 6x - 10y = 12 -----(iii)
==> 6x + 9y = 183 -----(iv)

Equating equations (iii) & (iv). We get ,

==> 6x + 9y - 6x + 10y = 183 - 12
==> 19y = 171
==> y = 171/19
==> y = 9

Putting the value of y in equation (ii). We get ,

==> 2x + 3(9) = 61
==> 2x + 27 = 61
==> 2x = 61 - 27
==> 2x = 34
==> x = 17

Perimeter of rectangle = 2(l+b)
=2(9+17)
=2(26)
=52 units