question
in the diagram below of triangle fgh, i is the midpoint of $\overline{fh}$ and j is the midpoint of $\overline{gh}$. if $ij = -7x + 44$, and $fg = 28 + 6x$, what is the measure of $\overline{ij}$?
answer attempt 1 out of 2
$ij = \square$

Question

Accepted Answer

# Explanation:
## Step1: Apply Midline Theorem
In triangle $FGH$, $I$ is the midpoint of $\overline{FH}$ and $J$ is the midpoint of $\overline{GH}$. By the Midline Theorem (also known as the Midsegment Theorem), the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. So, $IJ=\frac{1}{2}FG$.

## Step2: Set up the equation
We know $IJ = -7x + 44$ and $FG = 28 + 6x$. Substitute these into the midline theorem equation:
$$
-7x + 44=\frac{1}{2}(28 + 6x)
$$

## Step3: Solve for $x$
First, multiply both sides by 2 to eliminate the fraction:
$$
2(-7x + 44)=28 + 6x
$$
$$
-14x + 88 = 28 + 6x
$$
Add $14x$ to both sides:
$$
88=28 + 20x
$$
Subtract 28 from both sides:
$$
60 = 20x
$$
Divide both sides by 20:
$$
x = 3
$$

## Step4: Find the length of $IJ$
Substitute $x = 3$ into the expression for $IJ$:
$$
IJ=-7(3)+44
$$
$$
IJ=-21 + 44
$$
$$
IJ = 23
$$

# Answer:
$IJ = 23$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Apply Midline Theorem

Step2: Set up the equation

Step3: Solve for \(x\)

Step4: Find the length of \(IJ\)

Answer: