Using the Midsegment Theorem, the expression representing DE in triangle ABC with D and E as midpoints of sides AB and BC, respectively, and AC as 4x + 10, is 2x + 5. So, the correct answer is (2)
To find the expression that represents DE, we need to look at the properties of triangle ABC with points D and E being the midpoints of AB and BC, respectively. Given that CA equals 4x + 10, and D and E are midpoints, we can apply the Midsegment Theorem.
The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length. Therefore, DE is half the length of AC.
AC being 4x + 10 means DE would be (4x + 10) / 2, which simplifies to 2x + 5. Hence, the expression representing DE is 2x + 5.