Question

A rectangular sheet has an area 600 dm² and a perimeter 100 dm.Find the length of a sheet.
1. 30 dm or 20 dm
2. 50 dm or 10 dm
3. 40 dm or 20 dm
4. 10 dm or 60 dm

Answer 1

Correct Answer - Option 1 : 30 dm or 20 dm

Given

Area of sheet = 600 dm²

Perimeter of sheet = 100 dm

Formula used

Area of rectangle = Length × Breadth

Perimeter of rectangle = 2(length + Breadth)

Calculation

Area of sheet = 600 dm²

Length × breadth = 600

Breadth = 600/length

Perimeter of sheet = 2(length + breadth)

Where l is length of a rectangle.

100 = 2[l + (600/l)]

⇒  100 = 2[(l² + 600)/l]

⇒ 100 l = 2l² + 1200

⇒ 2l² - 100 l + 1200 = 0

⇒ l² - 50 l + 600 = 0

l⇒ ² - 30 l - 20 l + 600 = 0

⇒ l(l - 30) - 20(l - 30) = 0

⇒ (l - 30)(l - 20) = 0

⇒ l = 30 and l = 20

∴  length of a sheet could be 30 dm or 20 dm.