Question

the ratio of length to breadth of rectangular is 8:3 if the perimeter of the rectangle is 352cm than the sides of the rectangle are​

Answer 1

Let the length and breadth be 8x and 3x respectively.

Perimeter of rectangle = 2(l+b)

352cm = 2 (8x+3x)

352/2 = 8x+3x

176= 11x

176/11 = x

16cm = x

Length = 8x = 8×16 = 128cm

Breadth = 3x = 3×16 = 48cm

Hence, the sides of the rectangle are 128cm and 48cm.

Answer 2

Answer:

$\boxed{LENGTH = 128cm}$

$\boxed{BREADTH = 48cm}$

Step-by-step explanation

Solution

Here, the length to breadth ratio of a rectangle is given, i.e , 8:3

Therefore,

Let the length (l) of the rectangle be 8x

Let the breadth (b) of the rectangle be 3x

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 8x cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 3x cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

We are also given the perimeter of the rectangle which equals to 352 cm.

We know the equation for perimeter of a rectangle.

Perimeter of a rectangle =2(l+b)

∴ 2(l+b) =  352

We have ,

l = 8x and b = 3x

$\implies$ 2(8x+3x) = 352

$\implies$ 2 × 11x = 352

$\implies$ 22x = 352

∴ x = 352/22 = 16cm

∵ x = 16cm

Length = 8x = 8 × 16 = 128 cm.

Breadth = 3x = 3 × 16 = 48 cm.