Question

A rectangle carpet has on area of 120 m2 and perimeter is 46 m the length of ist diagonal is

Answer 1

Let length of carpet = L m

Breadth of carpet = B m

Given,

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

Hence, length of carpet is 15 m and breadth = 8 m

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