Perimeter of rectangle is 2.4 m less than $\frac{2}{5}$ 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 breath is $\frac{1}{3}$ of the length.

Given:

Perimeter of rectangle is 2.4 m less than $\frac{2}{5}$ of the perimeter of a square

Perimeter of the square = 40 m

Breadth of the rectangle = $\frac{1}{3}$ of the length of the rectangle

To find: Here we have to find the length and breadth of the rectangle.

Solution:

Let the length of the rectangle = 3a

So,

Breadth of the rectangle = $\frac{1}{3}\ \times$ 3a = a

Now,

Perimeter of the rectangle = 2(Length $+$ Breadth)

Perimeter of the rectangle = 2(3a $+$ a)

Perimeter of the rectangle = 2(4a)

Perimeter of the rectangle = 8a

Also, given that perimeter of rectangle is 2.4 m less than $\frac{2}{5}$ of the perimeter of the square:

Perimeter of the rectangle = $\frac{2}{5}$(Perimeter of the square) $-$ 2.4

8a = $\frac{2}{5}$(40) $-$ 2.4

8a = 16 $-$ 2.4

8a = 13.6

a = $\frac{13.6}{8}$

a = 1.7

So,

The length of the rectangle = 3a = 3 $\times$ 1.7 = 5.1 m

The breadth of the rectangle = a = 1.7 m

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Updated on: 10-Oct-2022

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