Question

in the diagram below of triangle $jkl$, $m$ is the midpoint of $overline{jl}$ and $n$ is the midpoint of $overline{kl}$. if $mn=-5x + 25$, and $jk = 35+5x$, what is the measure of $overline{mn}$?

Explanation:

Step1: Apply mid - segment theorem

By the mid - segment theorem in a triangle, $MN=\frac{1}{2}JK$.
So, $- 5x + 25=\frac{1}{2}(35 + 5x)$.

Step2: Solve the equation for x

Multiply both sides by 2: $2(-5x + 25)=35 + 5x$.
Expand: $-10x+50 = 35 + 5x$.
Add $10x$ to both sides: $50=35 + 15x$.
Subtract 35 from both sides: $15 = 15x$.
Divide by 15: $x = 1$.

Step3: Find the measure of MN

Substitute $x = 1$ into the expression for $MN$.
$MN=-5(1)+25$.
$MN=-5 + 25$.
$MN = 10$.

Answer:

10