Question

find the value of x.
3x + 21
21
x = □ (simplify your answer.)

Explanation:

Step1: Use the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length.
Let the mid - segment be related to the sides. If the length of one side is \(3x + 31\) and the other side (related by the mid - segment property) is \(2\times21\).

Step2: Set up the equation

We have the equation \(3x+31 = 2\times21\).
First, simplify the right - hand side: \(2\times21=42\).
So the equation becomes \(3x+31 = 42\).
Subtract 31 from both sides: \(3x=42 - 31\).
\(3x=11\).
Divide both sides by 3: \(x=\frac{11}{3}\).

Answer:

\(x = \frac{11}{3}\)