Question

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

Explanation:

Step1: Apply similar - triangle property

Since $\overline{TU}\parallel\overline{RS}$, $\triangle QTU\sim\triangle QRS$. Then, the ratios of corresponding sides are equal. That is, $\frac{QU}{QS}=\frac{QT}{QR}$.
We know that $QU = 8$, $QS=8 + 32=40$, $QT = 5$, and $QR=5 + x$.
So, $\frac{8}{40}=\frac{5}{5 + x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{8}{40}=\frac{5}{5 + x}$ gives us $8(5 + x)=40\times5$.
Expand the left - hand side: $40+8x = 200$.

Step3: Solve for $x$

Subtract 40 from both sides of the equation $40+8x = 200$: $8x=200 - 40$.
$8x = 160$.
Divide both sides by 8: $x=\frac{160}{8}=20$.

Answer:

$20$