Question

A rectangular carpet has an area of 120 sq metres and a perimeter of 46 metres. the length of its diagonal (in metres) 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

[ We assume length is larger than breadth . Well you can also write length = 8 m ]