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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