Answer:
Measure of DE is 12
Explanation:
Here, we want to get the measure of DE
We have two similar triangles here
BDE and BAC
if two triangles are similar, then the ratio of their sides are same
Thus, in this case, we proceed as follows;
Now, since DE cuts each side into half;
we can have AB as 2y; then BD as y
Thus, we have that;
BD/DE = AB/AC
y/4x + 4 = 2y/x + 36
2y(4x + 4) = y(x + 36)
2(4x + 4) = x + 36
8x + 8 = x + 36
8x-x = 36-8
7x = 28
x = 28/7
x = 4
recall;
DE is 4x + 4
insert x = 2
DE = 4(2) + 4
DE = 12