Question

Consider a square shaped paddy field with side of 48m. A pathway with uniforms breadth is surrounded the square field and the length of the outer side is 52m. Can you find the area of the pathway by using identities.

Answer 1

Algebraic Identity:

Difference of two squares  : a² - b² = (a + b) ( a - b)

Square paddy field

Length = 48 m

Area = Length²

Area = 48² m²

Paddy field with the path:

Length = 52 m

Area = Length²

Area = 52² m²

Find the area of the pathway:

Area of the pathway = Difference of the two area

Area of the pathway = 52²- 48²

Applying the algebraic Identify:

Area of the pathway = (52 + 48) (52 - 48)

Area of the pathway = (100) (4)

Area of the pathway = 400 m²

Answer: The area of the pathway is 400 m²