# The ratio of two sides of a parallelogram is 3:4. If its perimeter is 56cm, what are the lengths of the sides?

Dec 21, 2015

$12 , \text{16 cm}$

#### Explanation:

If the two sides have a ratio of $3 : 4$, that means their sides can be represented as $3 x$ and $4 x$, which also have a ratio of $3 : 4$.

Thus, if the sides of a parallelogram are $3 x$ and $4 x$, its perimeter is equal to the following expression:

$P = 2 \left(3 x\right) + 2 \left(4 x\right)$

The perimeter is $56$.

$56 = 2 \left(3 x\right) + 2 \left(4 x\right)$

Divide both sides by $2$.

$28 = 3 x + 4 x$

$28 = 7 x$

$x = 4$

Plug these back into our side lengths: $3 x$ and $4 x$

$3 \left(4\right) = \text{12 cm}$

$4 \left(4\right) = \text{16 cm}$