A rectangular carpet has an area of 120 m$$^2$$​ and a perimeter of 46 m. Find the length of its diagonal.

Correct option is C

Given:

Area = $$120 m^2$$​

perimeter = 46 m

Formula used:

Let the length of the rectangle be l

breadth of the rectangle be b

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

length of diagonal of rectangle (D) = $$D = \sqrt{l^2 + b^2} \\$$​

Solution:

As per the question,

Perimeter of rectangle = 2(l + b)

2(l + b) = 46

l + b = 23      ----(i)

Area of rectangle = l × b

l × b = 120

l = 120/b

Putting the value of l in eq. (i),

(120/b) + b = 23

=> 120 + b² = 23b

=> b² - 23b + 120 = 0

=> b² – 8b – 15b + 120 = 0

=> b(b – 8) – 15(b – 8) = 0

=> (b - 8)(b - 15) = 0

=> b = 8, 15

Let b = 8 m,

Then l = 23 - 8 = 15 m

Length of diagonal, 

$$D = \sqrt{l^2 + b^2} \\D = \sqrt{15^2 + 8^2} \\D = \sqrt{225 + 64} \\D = \sqrt{289}$$​

D = 17