# 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?

Aug 1, 2018

Length is $15 c m .$ and width is $10 c m .$

#### Explanation:

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

then perimeter is$2 \times \left(3 x + 2 x\right) = 2 \times 5 x = 10 x$

Hence $10 x = 50$

or $x = \frac{50}{10} = 5 c m .$

and length is $3 \times 5 = 15 c m .$ and width is $2 \times 5 = 10 c m .$

Aug 1, 2018

Length $l = 15 c m$

#### Explanation:

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

Let length$= l$ and width $= w$

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

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

$\frac{l}{w} = \frac{3}{2}$

$l = \frac{3}{2} w$ .....(2)

Substitute for $l$ in (1)
$P = 2 \cdot \left(\frac{3}{2} w\right) + 2 w = 5 w$

But $P = 50 c m$ so
$5 w = 50 c m$
$w = 10 c m$

Substitute $w = 10$ into (2)
$l = \frac{3}{2} \cdot 10 = 15$

Aug 1, 2018

$\text{length "=15" cm}$

#### Explanation:

$\text{sum the parts of the ratio } 3 + 2 = 5$

$P = 2 \left(l + b\right) = 50$

$l + b = \frac{50}{2} = 25$

$\frac{25}{5} = 5 \leftarrow \textcolor{b l u e}{\text{1 part}}$

$\text{length (l)"=5xx3=15" cm}$

$\text{breadth (b)"=5xx2=10" cm}$

$P = 2 \left(15 + 10\right) = 2 \times 25 = 50 \text{ cm}$