Question

A square contains four times the area of another square. If one side of the larger square is 4 cm greater than that of smaller square, then the perimeter of smaller square will be equal to

• A. 8 cm
• B. 16 cm
• C. 24 cm
• D. 32 cm

Answer 1

The correct option is B 16 cm

Let, side of smaller square = x cm.
$\therefore$ Side of larger square = (x + 4) cm
By the question; $(x+4{)}^2=4x^2$
$\Rightarrow x^2+8x+16=4x^2\Rightarrow 3x^2-8x-16=0\Rightarrow 3x^2-12x+4x-16=0\Rightarrow 3x(x-4)+4(x-4)=0\Rightarrow (x-4)(3x+4)=0,\therefore x=4cm$
$\Rightarrow$ Perimeter of smaller square = 4 $\times$ 4 = 16 cm