Question

IJ is a midsegment of AFGH. IJ = 9, FH=12, and GH = 15. Find the perimeter of AIJH. F The perimeter of AIJH is​

Answer 1

The perimeter of ΔIJH is 24 units.

To find the perimeter of ΔIJH, we need to determine the lengths of the sides AI, AJ, and AH.

Since IJ is a midsegment of triangle ΔFGH, it means that IJ is parallel to and half the length of side FG.

1. Find the length of FG:
`\(FG = 2 * IJ = 2 * 9 = 18\)` units.

2. Since GH = 15, and FH = 12, we can find the length of AH by subtracting FH from the length of FG:
`\(AH = FG - FH = 18 - 12 = 6\)` units.

3. Now, we have the lengths of AI, AJ, and AH. The perimeter (P) is the sum of all the sides:
`\(P = AI + AJ + AH\)`.

`\[P = 9 + 9 + 6 = 24\]` units.

Therefore, the perimeter of ΔIJH is 24 units.