The perimeter of a rectangle is 68 cm. If the area of the rectangle is 240 cm², then what is the length of each of its diagonals ?

26 cm

We know that,

Pythagoras theorem: Perpendicular² = Length² + Breadth²

Perimeter of Rectangle = 2(l + b)

We have,

Perimeter of a rectangle = 68 cm

Area of the rectangle = 240 cm²

So, 2(l + b) = 68

l + b = 34 ------ (A)

Area of rectangle = l × b

= l × b = 240 ------ (B)

From (1), we get l = 34 – b,

Then, (34 – b) × b = 240

= b² – 34b + 240 = 0

= b² – 10b – 24b + 240 = 0

= b(b – 10) – 24(b – 10) = 0

= (b – 24)(b – 10) = 0

= b = 10 or 24

Then, Length = 24 or 10 cm

Length of diagonal = \(\sqrt {24^2 + 10^2}\) = 26cm