Triangle Perimeter with Midsegment DE: Using 6, 8, and 10 Units

In order to calculate the perimeter of triangle $\triangle ADE$we need to find the lengths of its sides,

Let's now refer to the given information that $DE$is a median in $\triangle ABC$and therefore a median in a triangle equals half the length of the side it does not intersect, additionally we'll remember the definition of a median in a triangle as a line segment that extends from the midpoint of one side to the midpoint of another side, we'll write the property mentioned (a) and the fact derived from the given definition (b+c):

a.

$DE=\frac{1}{2}BC$b.

$AD=\frac{1}{2}AB$c.

$AE=\frac{1}{2}AC\\$Additionally, the given data in the drawing are:

d.

$BC=8$e.

$AB=6$f.

$AC=10$Therefore, we will substitute d', e', and f' respectively in a', b', and c', and we get:

g.

$DE=\frac{1}{2}BC=\frac{1}{2}\cdot8=4$h.

$AD=\frac{1}{2}AB=\frac{1}{2}\cdot6=3$i.

$AE=\frac{1}{2}AC=\frac{1}{2}\cdot10=5$

Therefore the perimeter of $\triangle ADE$ is:

j.

$P_{ADE}=DE+AD+AE=4+3+5=12$Therefore the correct answer is answer d.