If the diagonal of a square is √2 more than the side of the square,

1.	If the diagonal of a square is √2 more than the side of the square, then find the area of the square.1). 1 + √22). 2 + 2√23). 3 + 2√24). 4 + 3√2
Answer» As we know, DIAGONAL of a square = √2 × SIDE of square Let, side of square be ‘a’ cm Diagonal = a√2 = a + √2 ⇒ a√2 – a = √2 ⇒ a(√2 – 1) = √2 ⇒ a = √2/(√2 – 1) ⇒ a = √2/(√2 – 1) × (√2 + 1)/(√2 + 1) ⇒ a = (2 + √2)/(2 – 1) ⇒ a = 2 + √2 ∴ AREA of square = a² = (2 + √2)² = 4 + 2 + 4√2 = 6 + 4√2

If the diagonal of a square is √2 more than the side of the square, then find the area of the square.1). 1 + √22). 2 + 2√23). 3 + 2√24). 4 + 3√2

Answer»

As we know, DIAGONAL of a square = √2 × SIDE of square

Let, side of square be ‘a’ cm

Diagonal = a√2 = a + √2

⇒ a√2 – a = √2

⇒ a(√2 – 1) = √2

⇒ a = √2/(√2 – 1)

⇒ a = √2/(√2 – 1) × (√2 + 1)/(√2 + 1)

⇒ a = (2 + √2)/(2 – 1)

⇒ a = 2 + √2

∴ AREA of square = a² = (2 + √2)² = 4 + 2 + 4√2 = 6 + 4√2

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