Question

In a triangle, its midsegment is (2x + 8) units long and its parallel side is (5x - 9) units long. How long is the midsegment?

Answer 1

The midsegment is 58 units long.

Explanation:

Midsegment Theorem:

It states that the length of the midsegment is half the length of the parallel side.

In this question:

Midsegment: 2x + 8

Parallel side: 5x - 9

Parallel side is double the midsegment. So, we use this to find x:

`5x - 9 = 2(2x + 8)`

`5x - 9 = 4x + 16`

`x = 25`

Midsegment:

`2x + 8 = 2(25) + 8 = 50 + 8 = 58`

The midsegment is 58 units long.