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

$n+8=\dfrac{1}{2}(6n)$

$n+8=3n$

$8=3n-n$

$8=2n$

Divide both side by 2.

$\dfrac{8}{2}=n$

$4=n$

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

$5n=\dfrac{1}{2}(8n+10)$

$5n=4n+5$

$5n-4n=5$

$n=5$

Therefore, the value of n is equal to 5.