Question

The perimeter of a square S₁ is 12 m more than the perimeter of the square S₂. If the area of S₁ equals three times the area of S₂ minus 11, then what is the perimeter of S₁ ? 

(a) 24 m 

(b) 32 m 

(c) 36 m 

(d) 40 m

Answer 1

(b) 32 m

Let the perimeter of the square S₂ = \(x\) m, then perimeter of S₁ = (\(x\) + 12) m 

Length of one side of square S₂ = \(\frac{x}{4}\) m and

Length of one side of the square S₁ = (\(\frac{x}{4}\) + 3) m

given,  (\(\frac{x}{4}\) + 3)² = 3 (\(\frac{x}{4}\))² -11

⇒ \(\frac{x^2}{16}+9+\frac{3}{2}x=\frac{3x^2}{16}-11\)

⇒ \(\frac{x^2}{8}-\frac{3x}{2}-20=0\)

⇒ \(x\)² – 12\(x\) – 160 = 0 

⇒ \(x\)² – 20\(x\) + 8\(x\) – 160 = 0

⇒ \(x\)(\(x\) – 20) + 8(\(x\) – 20) = 0 

⇒ (\(x\) – 20) (\(x\) + 8) = 0  ⇒ \(x\) = 20 or –8 

Since negative values are impossible, x = 20

∴ S₂ = 20 m and S₁ = 32 m.