Question

s a midsegment of $\triangle pqs$.
pq = -18y + 68 and rt = 8y, what is the value of y?
(there is a triangle image with vertices p, s, q, and midsegment rt connecting t on ps and r on sq)

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of the midsegment of a triangle is half the length of the third - side. So, \(PQ = 2RT\).

Step2: Substitute the given expressions

Given \(PQ=-18y + 68\) and \(RT = 8y\), substitute into \(PQ = 2RT\):
\(-18y+68=2\times(8y)\)

Step3: Simplify the equation

\(-18y + 68=16y\)

Step4: Solve for \(y\)

Add \(18y\) to both sides:
\(68=16y + 18y\)
\(68=34y\)
Divide both sides by \(34\):
\(y=\frac{68}{34}\)

Answer:

\(y = 2\)