Question

The length of a rectangular park is 5 metres more than twice its breadth. If the area of the park is 250 sq. m, find the length and breadth of the park.

Answer 1

Let the breadth of the rectangular park be x cm.

Then, according to question

Length of the rectangular park be 2x + 5 cm.

Also, given area of rectangular park = 250 cm²

∴ 250 = x(2x + 5)

⇒ 2x² + 5x – 250 = 0

⇒ 2x² + 25x – 20x – 250= 0

⇒ x(2x + 25) – 10(2x + 25) = 0

⇒ (2x + 25)(x – 10) = 0

⇒ 2x + 25 = 0 and x – 10 = 0

⇒ x = `-25/2` and x = 10

∴ Breadth, x = 10 cm       ...(∵ x can't be negative)

Now, Length = 2(10) + 5 = 25 cm

Hence, the length of the park is 25 cm and breadth of the park is 10 cm.