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.

9.

It is given that:

Length of mid-segment = 54

Length of parallel side = 3n

By using mid-segment theorem for the given triangle, we get

`54=(1)/(2)(3n)`

`2* 54=3n`

`108=3n`

Divide both side by 3.

`(108)/(3)=n`

`36=n`

Hence, the value of n is equal to 36.

10.

It is given that:

Length of mid-segment = 4n+5

Length of parallel side = 74

By using mid-segment theorem for the given triangle, we get

`4n+5=(1)/(2)(74)`

`4n+5=37`

`4n=37-5`

`4n=32`

Divide both side by 4.

`n=(32)/(4)`

`n=8`

Hence, the value of n is equal to 8.