Question

DE is a mid segment of ABC if ac =3x-8 meters and DE = x + 2 meters solve for x

Answer 1

The value of x is 12 meters, found by setting up the equation 2(DE) = AC, where DE is the midsegment of triangle ABC and AC is the length of the opposite side.

Step-by-step explanation:

The question is about finding the value of x in the context of a midsegment of a triangle. A midsegment in a triangle is a segment that connects the midpoints of two sides of the triangle, and its length is half the length of the third side. In this case, DE is the midsegment of triangle ABC, which means that the length of DE is half the length of AC. Given that AC = 3x - 8 and DE = x + 2, we can set up the equation 2(DE) = AC to find the value of x.

To solve for x, we use the following steps:

1. Write the equation that relates DE and AC: 2(x + 2) = 3x - 8.
2. Distribute the 2 on the left side: 2x + 4 = 3x - 8.
3. Move terms involving x to one side and constants to the other: x = 12.

Therefore, the value of x is 12 meters.