Question

I need help with these

Answer 1

Given:

The figures of triangles and their mid segments.

To find:

The values of n.

Solution:

Mid-segment theorem: According to this theorem, mid segment of the triangle is a line segment that bisect the two sides of the triangle and parallel to third side, The measure of mid-segment is half of the parallel side.

11.

It is given that:

Length of mid-segment = n+8

Length of parallel side = 6n

Using mid-segment theorem, we get

`n+8=(1)/(2)(6n)`

`n+8=3n`

`8=3n-n`

`8=2n`

Divide both side by 2.

`(8)/(2)=n`

`4=n`

Therefore, the value of n is equal to 4.

12.

It is given that:

Length of mid-segment = 5n

Length of parallel side = 8n+10

Using mid-segment theorem, we get

`5n=(1)/(2)(8n+10)`

`5n=4n+5`

`5n-4n=5`

`n=5`

Therefore, the value of n is equal to 5.