Question

A rectangular carpet area 120 square metre and perimeter 46. The length of its diagonal is?​

Answer 1

Area of carpet = 120 m²

⇒Length × breadth = 120 m²

⇒ L × B = 120 ------(1)

Perimeter of carpet = 46 m

⇒ 2(Length + Breadth) = 46 m

⇒2(L + B) = 46 m

⇒L + B = 23 m

⇒ B = 23 - L , put it in equation (1)

L(23 - L) = 120

⇒23L - L² = 120

⇒L² - 23L + 120 = 0

⇒L² - 15L - 8L + 120 = 0

⇒L(L - 15) - 8(L - 15) = 0

⇒(L - 8)(L - 15) = 0

⇒L = 8, 15

Length of carpet is 15 m and breadth = 8 m

Diagonal=√{Length ²+breadth ²} = √{15²+8²}=17 m

Answer 2

Answer:

Area of carpet = 120 m²

⇒Length × breadth = 120 m²

⇒ L × B = 120 ------(1)

Perimeter of carpet = 46 m

⇒ 2(Length + Breadth) = 46 m

⇒2(L + B) = 46 m

⇒L + B = 23 m

⇒ B = 23 - L , put it in equation (1)

L(23 - L) = 120

⇒23L - L² = 120

⇒L² - 23L + 120 = 0

⇒L² - 15L - 8L + 120 = 0

⇒L(L - 15) - 8(L - 15) = 0

⇒(L - 8)(L - 15) = 0

⇒L = 8, 15

Length of carpet is 15 m and breadth = 8 m

Diagonal=√{Length ²+breadth ²} = √{15²+8²}=17 m