GATE2019 CE-1: GA-9

Question

A square has side $5$ 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. $8.50$ 

Answer 1

Let $x$ be the side of the larger square and $y$ be the side of the smaller square.

According to the question$:$

• $y=x-5\quad \rightarrow(1)$
• $x^2 =4y^2\rightarrow(2)$

Putting $(1)$ in $(2)$ we get

$x^2 = 4(x-5)^2$

$\implies x^{2}=4(x^{2}+25-10x)$

$\implies 3x^{2}-40x+100=0$

$\implies 3x^{2}-30x-10x+100=0$

$\implies 3x(x-10)-10(x-10)=0$

$\implies (x-10)(3x-10)=0$

$\implies x=10 \ cm \ \ (or) \ x = \dfrac{10}{3} \ cm$

So, the correct answer is $(C).$

Comments

x = 10 / 3  never possible because then smaller square side is negative.