Question

what equation would you set up to solve for x? a. x + 20 = x + 28 b. 2(x + 20) = x + 28 c. 2(x + 28) = x + 20 d. 2(x + 20) = 2(x + 28)

Explanation:

Step1: Identify the mid - segment theorem

In a triangle, a mid - segment (a line segment joining the mid - points of two sides of a triangle) is parallel to the third side and its length is half of the length of the third side. Here, $ZY$ is a mid - segment of $\triangle VUW$.

Step2: Set up the equation

If $ZY$ is the mid - segment of $\triangle VUW$, then the length of the mid - segment $ZY=x + 20$ and the length of the third side $UW=x + 28$. According to the mid - segment theorem, the length of the third side is twice the length of the mid - segment. So, $2(x + 20)=x + 28$.

Answer:

B. $2(x + 20)=x + 28$