The figure shows that segment ST is a midsegment of triangle PQR.
For this type of scenario, let's recall that the midsegment is equal to half of the length of the base of the triangle:
[tex]\text{Midsegment = }\frac{1}{2}(Base\text{ Length)}[/tex][tex]\text{ ST = }\frac{1}{2}PR[/tex][tex]\text{ 95 - 10x = }\frac{1}{2}(55\text{ - 5x)}[/tex][tex](95\text{ - 10x)(2) = }\frac{1}{2}(55\text{ - 5x)(2)}[/tex][tex]190\text{ - 20x = 55 - 5x}[/tex][tex]190\text{ - 55 = -5x + 20x}[/tex][tex]135\text{ = }15x\text{ }\rightarrow\text{ }\frac{135}{15}\text{ = }\frac{15x}{15}[/tex][tex]\text{ x = 9}[/tex]
Since we've determined that x = 9. let's solve for the measure of ST by plugging in x = 9 in the equation.
[tex]\text{ ST = 95 - 10x = 95 - 10(9)}[/tex][tex]\text{ ST = 95 - 9}0[/tex][tex]\text{ ST = 5}[/tex]
Therefore, ST = 5.
