Question

in △abc, points d and e are the midpoints of sides $overline{ab}$ and $overline{ac}$ respectively. it will be shown later in the course that $de=\frac{1}{2}bc$. if $ab = 12$, $bc = 18$, and $ac = 20$, then determine the perimeter of quadrilateral decb.

Explanation:

Step1: Find the length of DE

Since $DE=\frac{1}{2}BC$ and $BC = 18$, then $DE=\frac{1}{2}\times18 = 9$.

Step2: Find the lengths of BD and CE

Since D is the mid - point of AB and $AB = 12$, then $BD=\frac{1}{2}AB=\frac{1}{2}\times12 = 6$.
Since E is the mid - point of AC and $AC = 20$, then $CE=\frac{1}{2}AC=\frac{1}{2}\times20 = 10$.

Step3: Calculate the perimeter of DECB

The perimeter of quadrilateral DECB is $DE + EC+CB + BD$.
Substitute the values: $9+10 + 18+6=43$.

Answer:

43