# 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.

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### 4 Answers

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**

Given :

perimeter = 32

2[length + breadth] = 32

length + breadth = 16

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Sun of ratio = 5+3 = 8

**length =** 5/8 * 16 = **10 cm**

**breadth =** 3/8 * 16 = **6 cm **

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

Answer:

Length = 10 cm

Width = 6 cm

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.