# A is the midpoint of RM. If RA = 4x+3 and RM = 10x, what is the length of RM?

Oct 28, 2016

The length of RM is $30$.

#### Explanation:

Since A is the midpoint of RM,

RA $\cong$ AM

and

RM = RA + AM

Putting all this together, we have

$10 x = 4 x + 3 + 4 x + 3$
$10 x = 8 x + 6$
$10 x - 8 x = 8 x - 8 x + 6$
$2 x = 6$
$\frac{2 x}{2} = \frac{6}{2}$

$x = 3$

Now that we know the value of $x$, we can find the length of RM.

RM = $10 x$
RM = $10 \left(3\right)$
RM = $30$