Question

in the diagram below, $overline{tu}paralleloverline{rs}$. find the value of $y$. the diagram is not drawn to scale.

Explanation:

Step1: Apply similar - triangles property

Since $\overline{TU}\parallel\overline{RS}$, $\triangle QTU\sim\triangle QRS$ by the AA (angle - angle) similarity criterion (corresponding angles are equal because of parallel lines). For similar triangles, the ratios of corresponding sides are equal. That is, $\frac{QT}{QR}=\frac{QU}{QS}$.
We know that $QR = y$, $QT = 11$, $QU = 55$, and $QS=55 + 25=80$.
So, $\frac{11}{y}=\frac{55}{55 + 25}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{11}{y}=\frac{55}{80}$ gives us $55y=11\times80$.

Step3: Solve for $y$

First, calculate $11\times80 = 880$. Then, $y=\frac{880}{55}=16$.

Answer:

$16$