# The length and width of a rectangle are in the ration 5:3.. perimeter is 32 cm. Find length and width.Write an equation to solve it. Thank you.

Posted on

Let the length be "L" and the width "W"

We know that the ration is 5:3

Then, L/W = 5/3

Cross multiply:

==> 3L = 5W

==> L = (5/3)*W .......(1)

Also, it is given that the perimeter P is 32:

==> 2L + 2W = 32 .......(2)

Now substitute (1) in (2):

==> 2 (5/3)W + 2W = 32

==> (10/3)W + 2W = 32

==> (16/3)W = 32

Multiply by 3/16:

==> W = 32*3/16 = 6

==> W = 6 cm.

==> L = (5/3)w = (5/3)*6 = 10

==> L = 10 cm

Posted on

Given :

perimeter = 32

---------------------------------------------------------

Sun of ratio = 5+3 = 8

length = 5/8 * 16 = 10 cm

breadth = 3/8 * 16 = 6 cm

Posted on

Given that ratio of length and width is 5:3.

Length/Width = 5/3

==> Width = Length*(3/5)

Perimeter of a rectangle = 2*(Length + Width) = 32 cm (Given)

Substituting value of width as Length*(3/5) in above equation of perimeter:

2*(Length + Length*3/5) = 32

==> (16/5)*Length = 32

Therefore:

Length = 5*32/16 = 10 cm

Given ratio of length to width is 5:3

Therefore:

Width = Length*(3/5) = 10*3/5 = 6 cm

Length = 10 cm

Width = 6 cm

Posted on

length  and width are in the ratio 3:5 , the perimeter = 32.

Since perimeter is 2 times lthe sum of length and breadth,  the sum of the lenth and breadth = 32cm/2 = 16cm.

Now 16 cm could be divided into 5:3 ratio by:

{5/(5+3)}16cm and {3/(5+3)}16cm or

(5*16/8) cm and  (3*16/8)cm or

5*2 cm and 3*2cm

10 cm and 6 cm.

Therefore the length and breadth of the rectangle are 10cm and 6cm..

Check: the ratio of length and breadth 10cm : 6cm . Divide the two terms by 2cm  and the ratio is 10cm/2cm : 6cm/2cm . Or 5:3.

P = 2(length+breadth) = 2(10+6) = 32.