Question

triangle midsegment (algebraic)
score: 0.75/5 penalty: 0.25 off
question
in the diagram below of triangle fgh, i is the mid - point of fh and j is the mid - point of gh. if ij = 8x - 42, and fg=-20 + 8x, what is the measure of ij?
answer attempt 1 out of 2
ij =

Explanation:

Step1: Recall mid - segment theorem

The length of the mid - segment of a triangle is half the length of the third side. So, $IJ=\frac{1}{2}FG$.

Step2: Set up the equation

Given $IJ = 8x−42$ and $FG=-20 + 8x$. Then $8x−42=\frac{1}{2}(-20 + 8x)$.

Step3: Solve the equation

Multiply both sides by 2 to get $2(8x−42)=-20 + 8x$. Expand: $16x-84=-20 + 8x$. Subtract $8x$ from both sides: $16x-8x-84=-20$, which simplifies to $8x-84=-20$. Add 84 to both sides: $8x=-20 + 84$, so $8x = 64$. Divide both sides by 8: $x = 8$.

Step4: Find the length of $IJ$

Substitute $x = 8$ into the expression for $IJ$: $IJ=8x−42=8\times8−42=64 - 42=14$.

Answer:

$14$