Question

A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. the length of its diagonal is:

Answer 1

Let the length of rectangle be a

And width of rectangle be b

Area of rectangle = ab

=> ab = 120 ------(1)

Perimeter = 2 ( a+b)

=> a + b = 23

=> b = (23 - a) ------(2)

On substituting the value of b in equation 1, we get

a ( 23 - a) = 120

=> 23a - a^2 = 120

=> a^2 - 23a + 120 = 0

=> a^2 - 15a - 8a + 120 = 0

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

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

a = 15 and 8

If a = 15

b = 8

And,

When a = 8

b = 15

Diagonal = sqrt ( a^2 + b^2)

= sqrt ( 15^2 + 8^2)

= sqrt ( 225 + 64)

= sqrt ( 289)

= 17 cm