Question

The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm2 less than the area of the rectangle.

Answer 1

Answer:

36 cm.

Step-by-step explanation:

Let, the side of the square = x cm.

As, side of the square is 3 cm less than and 2 cm more than the sides of the rectangle.

Thus, the sides of the rectangle will be (x+3) and (x-2)

Also, it is given that, 'The area of the square is 30 cm² less than the area of the rectangle'.

As, Area of the square = $x^{2}$

Area of the rectangle = $(x+3)(x-2)$

Thus, we have

$(x+3)(x-2)-x^{2}=30$

i.e. $x^2-2x+3x-6-x^{2}=30$

i.e. $x-6=30$

i.e. $x=36$

Thus, the side of the square is 36 cm.