Question

find the perimeter of △vwx. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Determine similarity of triangles

Since two - angle pairs in $\triangle UST$ and $\triangle VWX$ are equal ($50^{\circ}$ and $70^{\circ}$), the two triangles are similar by the AA (angle - angle) similarity criterion.

Step2: Set up proportion for side lengths

The ratios of corresponding sides of similar triangles are equal. Let's assume the correspondence: $\frac{US}{VW}=\frac{ST}{WX}=\frac{TU}{XV}$. We know $US = 16$, $ST=22$, $TU = 25$, $VW = 33$, $XV=24$. Let's find $WX$ using the proportion $\frac{US}{VW}=\frac{ST}{WX}$. Substituting the values, we have $\frac{16}{33}=\frac{22}{WX}$, then $16WX=22\times33$, and $WX=\frac{22\times33}{16}=\frac{726}{16}=45.375$.

Step3: Calculate the perimeter of $\triangle VWX$

The perimeter $P$ of $\triangle VWX$ is $P = VW+WX + XV$. Substitute $VW = 33$, $WX=45.375$, and $XV = 24$ into the formula. $P=33 + 45.375+24=102.375\approx102.4$.

Answer:

$102.4$