Question

the area of the square is 4x^2 + 20x +25, find its side​.

Answer 1

Area of Square = 4x² + 20x + 25

⇒ Area of Square = Side × Side

⇒ 4x² + 20x + 25 = Side × Side

⇒ 4x² + 20x + 25 = (Side)²

⇒ √(4x² + 20x + 25) = √(Side)²

⇒ √(4x² + 20x + 25) = Side

⇒ √(2²x² + 20x + 5²) = Side

⇒ √((2x)² + 2 × 2x × 5 + 5²) = Side

⇒ √(2x + 5)² = Side

⇒ 2x + 5 = Side

⇒ Side = 2x + 5

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Answer 2

Area = 4x² + 20x + 25

We know that

Area of Square = Length × Breadth

Let's factorize the given equation to find the side

4x² + 20x + 25

⇒ 4x² + 10x + 10x + 25

⇒ 2x(2x + 5) + 5(2x + 5)

⇒ (2x + 5)(2x + 5)

⇒ (2x + 5)²

Area = 4x² + 20x + 25

→ Area = (2x + 5)²

→ (Side)² = (2x + 5)²

Taking square Root on both sides,

Side = (2x + 5) units

Additional Information:

• Perimeter of a square = 4 × Side
• In square all sides are equal.
• In rectangle, opposite sides are equal.