Question

Perimeter of rectangle is 2.4m less than 2/5 of the perimeter of a square. If the perimeter of the square is 40m, find the length and breadth of the rectangle given that breadth is 1/3 of the length.

Answer 1

2/5 of 40 is 16 Perimeter of rectangle is 16-2.4 i.e 13.6 l length of rectangle is x breath of rectangle is 1/3x Perimeter of rectangle is 2(l+b) 2(x+1/3x)=13.6 4/3x=13.6/2 4/3x=6.8 x=68/10×3/4 x=5.1 breath is 1/3 of length i.e 2.7 Length=5.1 Breath=2.7

Answer 2

The ‘length and breadth’ of the rectangle is 5.1m & 1.7m.

To find:

Length and breadth of the rectangle = ?

Solution:  

Given: Perimeter of rectangle is 2.4m less than $\frac{2}{5}$ of the ‘perimeter of a square’. Perimeter of the square is 40m and breadth is $\frac{1}{3}$ of the length.

Perimeter of square = 4 sides = 40m

Let's assume length of rectangle be x m, then, breadth  $=\frac{x}{3} m$

Formula to find perimeter of rectangle = 2 (length + width)

Hence,

$2(l+b)=\frac{2}{5} \times 40-2.4$

$2\left(x+\frac{x}{3}\right)=2 \times 8-2.4$

$2\left(3 x+\frac{x}{3}\right)=13.6$

$2 \times \frac{4 x}{3}=13.6$

$4 x=13.6 \times \frac{3}{2}$

$4 x=20.4$

$x=\frac{20.4}{4}$

$x=5.1 m$

So, length = x = 5.1 m

Then, breadth $=\frac{x}{3}=\frac{5.1}{3}\bold{=1.7 m}$