Question

From a rectangular sheet of paper, two squares are cut off as shown below:

The remaining rectangle should have area 24 squares centimetres. What should be the lengths of the sides of the squares?

Answer 1

Let the length of the side of one square be x cm.

Length of the side of two squares = (x + x) cm = 2x cm

∴ Length of the remaining rectangle = (16 − 2x) cm

Breadth of the remaining rectangle = Length of the side of square = x cm

Area of the remaining rectangle = 24 cm²

⇒ Length × Breadth = 24 cm²

⇒ (16 − 2x)x = 24

⇒ 16x −2x² = 24

⇒ 8x − x² = 12

⇒ x² − 8x = −12

Adding 16 to both the sides to make L.H.S a perfect square:

x² − 8x + 16 = −12 + 16

⇒ x² − 2 × 4 × x + (4)² = 4

⇒ (x − 4)² = 4 {Using a² + b² − 2ab = (a − b)²}

Thus, the length of the sides of the squares can be 6 cm or 2 cm.

It can be observed from the figure that the length of the remaining rectangle should be less than the length of the side of the square. So, x cannot be equal to 2.

Hence, the length of the sides of the square should be 6 cm.