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

$54=\dfrac{1}{2}(3n)$

$2\times 54=3n$

$108=3n$

Divide both side by 3.

$\dfrac{108}{3}=n$

$36=n$

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

$4n+5=\dfrac{1}{2}(74)$

$4n+5=37$

$4n=37-5$

$4n=32$

Divide both side by 4.

$n=\dfrac{32}{4}$

$n=8$

Hence, the value of n is equal to 8.