Question

A rectangle has a perimeter of 50 cm. If the ratio of its length to its width is 3:2, find the length of the rectangle?

Answer 1

Length is `15cm.` and width is `10cm.`

Explanation:

As length and width are in the ratio of `3:2`, let these be `3x` and `2x`

then perimeter is`2xx(3x+2x)=2xx5x=10x`

Hence `10x=50`

or `x=50/10=5cm.`

and length is `3xx5=15cm.` and width is `2xx5=10cm.`

Answer 2

Length `l =15cm`

Explanation:

Perimeter #(P) is the total distance around the sides.

Let length`= l` and width `= w`

`P = 2l + 2w` .....(1)

We are told that the ratio of `l` to `w` is `3:2` so

`l/w = 3/2`

`l = 3/2w` .....(2)

Substitute for `l` in (1)
`P = 2*(3/2w) + 2w = 5w`

But `P = 50cm` so
`5w = 50cm`
`w = 10 cm`

Substitute `w = 10` into (2)
`l = 3/2*10 =15`

Answer 3

`"length "=15" cm"`

Explanation:

`"sum the parts of the ratio "3+2=5`

`P=2(l+b)=50`

`l+b=50/2=25`

`25/5=5larrcolor(blue)"1 part"`

`"length (l)"=5xx3=15" cm"`

`"breadth (b)"=5xx2=10" cm"`

`P=2(15+10)=2xx25=50" cm"`