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. 

∴ 3(x + 4) × x = (x + 4)²

⇒ 3x² + 12x = (x + 4)²

⇒ 3x² + 12x = x² + 8x + 16 

⇒ 2x² + 4x – 16 = 0 

⇒ x² + 2x – 8 = 0 

⇒ x² + (4 – 2)x – 8 = 0 

⇒ x² + 4x – 2x – 8 = 0 

⇒ x(x + 4) – 2(x + 4) = 0 

⇒ (x + 4)(x – 2) = 0 

⇒ x = –4 or x = 2 

∴ 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.