Question

Perimeter of a rectangle is 2 m less than 2/5 of the perimeter of a square. If the perimeter
of the square is 40 m, find the length and breadth of the rectangle given that the breadth
is 1/3 of the length.​

Answer 1

Given : Perimeter of rectangle is 2 less than the 2/5 of the perimeter of square.

i.e.

Perimeter of rectangle = 2/5 Perimeter of square - 2

Perimeter of square = 40 m and breadth of the rectangle is 1/3 of the length of rectangle.

i.e.

Breadth = 1/3 Length

Find : Length and breadth of the rectangle.

Solution :

Perimeter of rectangle = 2/5 perimeter of square - 2

Perimeter of rectangle = 2(l + b)

Perimeter of square = 40

So,

=> 2(l + l/3) = 2/5 × 40 - 2

=> 2(l + l/3) = 80/5 - 2

=> 2(l + l/3) = 16 - 2

=> 2(l + l/3) = 14

=> l + l/3 = 7

=> 4l/3 = 7

=> 4l = 21

=> l = 5.25

So,

=> b = 1/3 × l

=> b = 1/3 × 5.25

=> b = 1.75

∴ Length of rectangle is 5.25 m and Breadth of rectangle is 1.75 m.