Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 5 - Relationships Within Triangles - 5-1 Midsegments of Triangles - Practice and Problem-Solving Exercises - Page 290: 35

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: $P = 18.5$
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