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

Sagot :

Answer:

The midsegment is 58 units long.

Step-by-step 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:

[tex]5x - 9 = 2(2x + 8)[/tex]

[tex]5x - 9 = 4x + 16[/tex]

[tex]x = 25[/tex]

Midsegment:

[tex]2x + 8 = 2(25) + 8 = 50 + 8 = 58[/tex]

The midsegment is 58 units long.

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