The area of a rectugular carpet is 120m2and its perimeter is 46 m,then find its diagonal

Hi!

Let length of carpet = L m
Breadth of carpet = B m

Given,
Area of carpet = 120 m?
?Length ? breadth = 120 m?
? 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 - L? = 120
?L? - 23L + 120 = 0
?L? - 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 ?+breadth ?} = ?{15?+8?}=17 m

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

Regards!