Question

The area of a rectangle is (14x² – 29xy – 15y²) sq units. Find its sides and the perimeter of the rectangle.

Answer 1

Given: area of the rectangle = (14x² – 29xy – 15y²) sq. units.

Here we need to split the middle term (29) as sum of difference of two terms, whose product equals to 14 × 15 = 210

Therefore, (14x² – 29xy – 15y²) = (14x² – 35xy + 6xy – 15y²)

⇒ 7x(2x – 5y) + 3y(2x – 5y)

⇒ (7x + 3y) (2x – 5y)

If length is (7x + 3y), then breadth is (2x – 5y)

We know that the perimeter of a rectangle = 2l + b

⇒ 27x + 3y + 2x – 5y 

⇒ 29x – 2y

⇒ 18x – 4y

The perimeter of a rectangle = (18x – 4y)

Hence, the sides of the rectangle are (7x + 3y) and (2x – 5y) and its perimeter is (18x – 4y).