# If two segments AB and CD are in the ratio 3:5 andCD is longer than AB by 28 cm, how long is each segment?

Apr 2, 2015

$\left\mid A B \right\mid = 42$ $c m$ and $\left\mid C D \right\mid = 70$ $c m$

Lets say that the length of $A B$ is $l$ and the length of $C D$ is $m$.

We know these:

$\frac{l}{m} = \frac{3}{5}$

$m = l + 28$

So we can find the value of $l$

Lets replace $m$ with $l + 28$ in the first equation.

$\frac{l}{l + 28} = \frac{3}{5}$

$5 l = 3 \cdot \left(l + 28\right)$
$5 l = 3 l + 84$
$2 l = 84$
$l = 42$ $c m$

Now we know the value of $l$, we knew that $m = l + 28$ so:

$m = 42 + 28$
$m = 70$ $c m$