Length of a rectangle is 17 m more than its breadth. If length of its diagonal is 25 m, then find the perimeter of the rectangle?

GIVEN:

Length of a rectangle is 17 m more than its breadth.

Length of its diagonal = 25 m

CONCEPT:

Mensuration

FORMULA USED:

Perimeter of rectangle = 2(l + b)

CALCULATION:

Let the breadth of rectangular field = ‘x’ m

So, the length of rectangular field = (x + 17) m

From the question:

(x + 17)² + x² = 25²

⇒ x² + 289 + 34x + x² = 625

⇒ x² + 17x – 168 = 0

⇒ x² + 24x – 7x – 168 = 0

⇒ x(x + 24) – 7(x + 24) = 0

⇒ x = 7

Hence,

Breadth of rectangle = 7 m

Length of rectangle = 7 + 17 = 24 m

Perimeter of rectangle = 2 × (7 + 24)

⇒ 62 m

Therefore the correct answer is 62m.