Two squares have sides x and (x + 4) cm. The sum of their area is 656

1.	Two squares have sides x and (x + 4) cm. The sum of their area is 656 cm2. Find the sides of the square.
Answer» Let S₁ and S₂ be the two squares. And, let x cm be the side square S₁ and (x + 4) cm be the side of the square S₂. So, Area of the square S₁ = x² cm² Area of the square S₂ =(x + 4)² cm² From the question, we have Area of the square S₁+ Area of the square S₂= 656 cm² ⇒ x² cm²+ (x + 4)² cm²= 656 cm² x²+ x²+ 16 + 8x – 656 = 0 2x²+ 16 + 8x – 656 = 0 2(x²+ 4x – 320) = 0 x²+4 x – 320 = 0 x²+ 20x – 16x – 320 = 0 x(x + 20) – 16(x + 20) = 0 (x + 20)(x – 16) = 0 Now, either x + 20 = 0 ⇒ x = -20 Or, x – 16 = 0 ⇒ x = 16 As the value of x cannot be negative, we choose the value of x = 16 ⇒ x + 4 = 20 Therefore, The side of the square S₁= 16 cm The side of the square S₂ = 20 cm

Two squares have sides x and (x + 4) cm. The sum of their area is 656 cm2. Find the sides of the square.

Answer»

Let S₁ and S₂ be the two squares.

And, let x cm be the side square S₁ and (x + 4) cm be the side of the square S₂.

So,

Area of the square S₁ = x² cm²

Area of the square S₂ =(x + 4)² cm²

From the question, we have

Area of the square S₁+ Area of the square S₂= 656 cm²

⇒ x² cm²+ (x + 4)² cm²= 656 cm²

x²+ x²+ 16 + 8x – 656 = 0

2x²+ 16 + 8x – 656 = 0

2(x²+ 4x – 320) = 0

x²+4 x – 320 = 0

x²+ 20x – 16x – 320 = 0

x(x + 20) – 16(x + 20) = 0

(x + 20)(x – 16) = 0

Now, either x + 20 = 0 ⇒ x = -20

Or, x – 16 = 0 ⇒ x = 16

As the value of x cannot be negative, we choose the value of x = 16 ⇒ x + 4 = 20

Therefore,

The side of the square S₁= 16 cm

The side of the square S₂ = 20 cm