A square has sides 5 cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square

Q. A square has sides 5 cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is cm.

(A) 18.50

(B) 15.10

(C) 10.00

(D) 8.50

Ans: 10.00

Solution:

Given:  The side of small square is 5 cm less than larger one. 

Area of large square is 4 times of area of small square. 

Let, 

Side of large square = x

 side of small square = x – 5 

∵ Area of large square = 4 × Area of small square 

⇒ x2 = 4 × (x – 5)2 

⇒ x2 = 4 (x2 – 10x + 25) 

⇒ 3×2 – 40x + 100 = 0 

⇒ 3×2 – 30x – 10x + 100 = 0 

⇒ 3 × (x – 10) – 10 × (x – 10) = 0 

⇒ x – 10 = 0; 3x – 10 = 0 

∴ x = 10 or x = 10/3 = 3.33 

But x = 3.33 gives negative value of side of smaller square. 

∴ x = 10 cm