Question

If the area of a square is 400 m², then find the side of the square by the method of factorization.

Answer 1

Let the side of the square be x meter.

Then, Area of a square = side × side = x × x = x²

According to the question,

x² = 400

⇒ x² – 400 = 0

⇒ x² – (20)² = 0

⇒ (x + 20) (x – 20) = 0  ......[∵ a² – b² = (a + b) (a – b)]

⇒ (x + 20) = 0 or (x – 20) = 0

⇒ x = – 20 or x = 20

Because a square's side cannot be negative, x = 20.

As a result, the side of the square is 20 m.