Question

If one side of a square is increased by 3 m and the other side is reduced by 2 m.,a rectangle is formed whose area is 4 m 2 more than the area of the original square. Find the side of the original square.

Answer 1

Let x be the side of the square.

Area of the square= x^2

Area of the rectangle
= length * breadth
= (x+3)(x-2)

Given that area if the rectangle is 4 m.sq more than area of the square

(x+3)(x-2)= (x^2) + 4

(x^2) + 3x - 2x -6 = (x^2) + 4

(x^2) + x -6 = (x^2) + 4

x -6 = 4

x= 4+6
x=10

Answer 2

Hi ,

Let side of the square = a m

If one side of a square is increased by 2 m

and other side is reduced by 2 m , a rectangle

is formed

Dimensions of the rectangle

length = ( a + 2 ) m

Breadth = ( a - 2 ) m

According to the problem given ,

Perimeter of the rectangle = 48 m

2( l + b ) = 48

2 [ a + 2 + a - 2 ] = 48

2 × 2a = 48

4a = 48

a = 48 / 4

a = 12

Therefore side of the original

square = a = 12m

I hope this helps you.

:)