Answer
The perimeter of $\triangle IJH$ IS $18.5$.
Work Step by Step
In order to find the perimeter of $\triangle IJH$, we need to find the lengths of all its sides. Since we know $I$ is the midpoint of $\overline{FH}$ and $J$ is the midpoint of $\overline{GH}$, $\overline{HJ}$ is half of $\overline{GH}$, and $\overline{HI}$ is half the length of $\overline{FH}$. We are already have the length of $\overline{IJ}$, so we just need the length of the other two sides of $\triangle IJH$.
Let's find $HJ$ by dividing $GH$ in half:
$GH = 2(HJ)$
Let's plug in the value for $GH$:
$13 = 2(HJ)$
Divide each side of the equation by $2$ to solve for $HJ$:
$HJ = 6.5$
Let's find $HI$ by dividing $FH$ in half:
$FH = 2(HI)$
Let's plug in the value for $FH$:
$10 = 2(HI)$
Divide each side of the equation by $2$ to solve for $HI$:
$HI = 5$
Now, we can find the perimeter of the triangle, which is the sum of all the sides of the triangle:
$P = HJ + HI + IJ$
Let's plug in the values for each of the sides.
$P = 6.5 + 5 + 7$
Add from left to right:
$P = 18.5$
