Question

What value of x satisfies the midsegment theorem given the segment lengths: (RG = 4x - 65) and (SH = 2x - 4)?

A) x = 26
B) x = 15
C) x = 31
D) x = 35

Answer 1

The value of x that satisfies the midsegment theorem is x = 30.5. Hence, A) is correct.

Step-by-step explanation:

The midsegment theorem states that the midsegment of a triangle is parallel to the third side and half its length. In this case, the midsegment is the line connecting the midpoints of the sides RG and SH.

Let's set up an equation using the given segment lengths: RG = 4x - 65 and SH = 2x - 4.

According to the midsegment theorem, the midsegment should have a length equal to half the sum of the segment lengths, so: (4x - 65) + (2x - 4) = 2(2x - 4).

Solving this equation, we get: 6x - 69 = 4x - 8. Simplifying, we find: 2x = 61. Dividing both sides by 2, we find the value of x: x = 30.5.