Answer :

Let x and y be the original length and breadth

Length of a rectangle is 5 cm less then twice its breadth,

x = 2y – 5

If the length is decreased by 3 cm and breadth increased by 2 cm the perimeter is 72.

2(x – 3) + 2(y + 2) = 72

Dividing the equation by 2

⇒ x – 3 + y + 2 = 36

⇒ x + y – 1 = 36

⇒ x + y = 37

Replace x with (2y – 5)

⇒ (2y–5) + y = 37

⇒ 3y = 37 + 5

⇒ 3y = 42

y = 14 cm is the original width

For x,

⇒ x = 2(14) – 5

⇒ x = 28 – 5

x = 23 cm is the original length

Area of original rectangle.

23 × 14 = 322 sq cm.

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