Find the length of the midsegment.

C. Use the Pythagorean theorem. a^2 + b^2 = c^2

You have the a^2 and c^2 so do c^2 - a^2 to get b^2.

Then find the square root of b then subtract 2 then divide it by 5
Then use math to find the midsegment.

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DelcieRiveria DelcieRiveria · Answer 2 · 2019-06-14T11:37:03+02:00

Answer:

The length of the mid segment is 22 units.

Step-by-step explanation:

A line segment is called a mid segment of a triangle if

1. It connect the midpoints of two sides of a triangle.

2. It is always parallel to the third side.

3. The length of the midsegment is half the length of the third side.

From the given figure it is clear that the length of mid segement is 5x+2 and the length of third side is 3x+32. It means 5x+2 is half of 3x+32.

[tex]5x+2=\frac{1}{2}\times (3x+32)[/tex]

Multiply both sides by 2.

[tex]2(5x+2)=(3x+32)[/tex]

Using distributive property.

[tex]10x+4=3x+32[/tex]

Subtract 4 from both the sides.

[tex]10x=3x-32+4[/tex]

Subtract 3x from both the sides.

[tex]10x-3x=28[/tex]

[tex]7x=28[/tex]

Divide both sides by 7.

[tex]x=4[/tex]

The value of x is 4. The length of mid segment is

[tex]5x+2=5(4)+2=22[/tex]

Therefore the length of the mid segment is 22 units.