Final answer:
DE in triangle ABC is parallel to BC and can be found using the Midpoint Theorem.
Step-by-step explanation:
In triangle ABC, D is the midpoint of side AB and E is the midpoint of side BC. Since D is the midpoint of AB, we can say that AD = DB. Similarly, since E is the midpoint of BC, we have BE = EC. In triangle ABC, AC is the hypotenuse and DE is a line segment connecting the midpoints of the other two sides.
Therefore, using the Midpoint Theorem, we know that DE is parallel to BC and it is half the length of BC. So, DE = 0.5 * BC.
Given that AC = 4x + 10, we need to find an expression that represents DE in terms of x.
Let's find BC first. In triangle ABC, we have AC as the hypotenuse, so using the Pythagorean Theorem, we can write:
AC^2 = AB^2 + BC^2
(4x + 10)^2 = (2x)^2 + BC^2
Simplifying this equation will give us the value of BC. Once we have BC, we can substitute it into DE = 0.5 * BC to get the expression for DE in terms of x.
Learn more about Midpoint Theorem