Question

What is HB? Triangle Mid-segment Theorem

Answer 1

HB = 13

Explanation:

In triangle GHJ, points A, B, C are mid points of the sides GH, HJ, GJ respectively.

Therefore by Mid-segment Theorem.

`AC = (1)/(2) HJ \\ \\ 3y - 5 = (1)/(2) (4y + 2) \\ \\ 3y - 5 = (1)/(2) * 2 (2y + 1) \\ \\ 3y - 5 = 2y + 1\\ \\ 3y - 2y = 5 + 1 \\ \\ y = 6 \\ \\ HJ = 4y + 2 \\ \\ HJ = 4 * 6 + 2 \\ \\ HJ = 24 + 2 \\ \\ HJ = 26 \\ \\ HB= (1)/(2) HJ \\ \\ HB= (1)/(2) * 26 \\ \\ \huge \red{ \boxed{ HB= 13}}`