#### Question

Two squares have sides x cm and (x + 4) cm. The sum of their area is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.

#### Solution

Given that, two squares have sides x cm and (x + 4) cm.

Sum of their area = 656 cm^{2}

∴ x^{2} + (x + 4)^{2} = 656

x^{2} + x^{2} + 16 + 8x = 656

2x^{2} + 8x – 640 = 0

x^{2} + 4x – 320 = 0

x^{2} + 20x – 16x – 320 = 0

x(x + 20) – 16(x + 20) = 0

(x + 20) (x – 16) = 0

x = -20, 16

But, x being side, cannot be negative.

So, x = 16

Thus, the sides of the two squares are 16 cm and 20 cm.

Is there an error in this question or solution?

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Two Squares Have Sides X Cm and (X + 4) Cm. the Sum of Their Area is 656 Sq. Cm. Express this as an Algebraic Equation in X and Solve the Equation to Find the Sides of the Squares. Concept: Quadratic Equations.

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