Question

question in the diagram below of triangle jkl, m is the mid - point of $overline{jl}$ and n is the mid - point of $overline{kl}$. if $mn = 2x+13$, and $jk=-2x + 38$, what is the measure of $mn$? answer attempt 1 out of 2 $mn=square$

Explanation:

Step1: Apply mid - segment theorem

By the mid - segment theorem in a triangle, the length of the mid - segment (the line segment connecting the mid - points of two sides of a triangle) is half the length of the third side. So, $MN=\frac{1}{2}JK$.

Step2: Set up the equation

We have $2x + 13=\frac{1}{2}(-2x + 38)$.

Step3: Solve the equation

Multiply both sides by 2: $2(2x + 13)=-2x + 38$. Expand to get $4x+26=-2x + 38$. Add $2x$ to both sides: $4x + 2x+26=-2x+2x + 38$, which simplifies to $6x+26 = 38$. Subtract 26 from both sides: $6x+26 - 26=38 - 26$, so $6x = 12$. Divide both sides by 6: $x = 2$.

Step4: Find the length of $MN$

Substitute $x = 2$ into the expression for $MN$: $MN=2x + 13=2\times2+13=4 + 13=23$.

Answer:

23