Question

The breadth of a rectangle is 5cm less than its length. If the length and breadth are both increased by 2cm, then the new area becomes 26cm2 more than the old area. Find the length and breadth of the rectangle.

Answer 1

Step-by-step explanation:

Case 1:-

Let the length of the rectangle be x cm

As, breadth is 5cm less than length

Breadth of the rectangle = (x - 5)cm

Area of the rectangle = Length × Breadth

= x (x - 5)

= x² - 5x

Area of the rectangle = (x² - 5x)

Case 2:-

If length and breadth are increased by 2cm

Length becomes = (x + 2)cm

Breadth becomes = x - 5 + 2 = (x - 3)cm

Area of the new rectangle :-

= (x + 2) (x - 3)

= x² - 3x + 2x - 6

= x² - x - 6

Area of the new rectangle = x² - x - 6

Given, the new area becomes 26cm² more than the old area

⇢ x² - x - 6 = x² - 5x + 26

⇢ x² - x² - x + 5x = 26 + 6

⇢ 4x = 32

⇢ x = 32/4 = 8

Length of the rectangle = x = 8cm

Breadth of the rectangle = x - 5 = 8 - 5 = 3cm