Question

triangle midsegment (algebraic)
score: 0/5 penalty: 0.25 off
question
in the diagram below of triangle efg, h is the mid - point of eg and i is the mid - point of fg. if hi=-4x + 45, and ef = 25+5x, what is the measure of hi?
answer attempt 1 out of 2
hi=

Explanation:

Step1: Recall mid - segment theorem

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

Step2: Set up the equation

We have $- 4x + 45=\frac{1}{2}(25 + 5x)$.

Step3: Multiply both sides by 2

$2(-4x + 45)=25 + 5x$.
$ - 8x+90 = 25 + 5x$.

Step4: Move x terms to one side

$-8x - 5x=25 - 90$.
$-13x=-65$.

Step5: Solve for x

$x = 5$.

Step6: Find the measure of HI

Substitute $x = 5$ into the expression for $HI$: $HI=-4x + 45=-4\times5+45=-20 + 45=25$.

Answer:

$25$