Question

a rectangular carpet has area 120 sq MTR and perimeter 46 mtr. the length of its diagonal is ??​

Answer 1

Answer:

Let length of carpet = L m

Breadth of carpet = B m

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 = 15 m

Breadth = 8 m

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

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