Question

The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.

Answer 1

Let the breadth of rectangle be x cm. 

According to the question:

Side of the square = (x + 4)cm

Length of the rectangle = \(\{\)3(x + 4)\(\}\)cm

It is given that the areas of the rectangle and square are same.

∴ x = 2

(∵The value of x cannot be negative)

Thus, the breadth of the rectangle is 2 cm and length is \(\{\)3(2 + 4) = 18\(\}\)cm.

Also, the side of the square is 6 cm.

Answer 2

Let the breadth of rectangle be x cm. 

According to the question:

Side of the square = (x+4) cm

Length of the rectangle = {3(x+4)} cm

It is given that the areas of the rectangle and square are same.

Thus, the breadth of the rectangle is 2 cm and length is {3(2 + 4) =18} cm. 

Also, the side of the square is 6 cm