Question

if one side of a rectangle is reduced by 2 cm , it becomes a square and the area of rectangle reduces by 100 cm square . find the area of rectangle.

Answer 1

Let the side of rectangle be x cm.

If it is reduced by 2 then is becomes square so other side rectangle = (x-2)cm

Area=x(x-2) cm^2

Area of square=(x-2)(x-2)cm^2

According to question,

(x-2)(x-2)+100=x(x-2)

x^2+4-4x+100=x^2-2x

104-4x=-2x

2x=104

x=52cm

Area=x(x-2)cm^2

=52*50cm^2

=2600cm^2

This is the required answer if the calculation is correct.