Question

1. solve for x. δabc～δwrg
2. express in simplest radical form: √50

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle WRG$, the ratios of corresponding sides are equal. So, $\frac{AB}{WR}=\frac{BC}{RG}$. Substituting the given values, we get $\frac{320 + 4x}{120}=\frac{1410}{80}$.

Step2: Cross - multiply

Cross - multiplying gives us $80(320 + 4x)=120\times1410$.
Expanding the left - hand side: $80\times320+80\times4x = 25600+320x$. And $120\times1410 = 169200$. So, $25600 + 320x=169200$.

Step3: Solve for x

First, subtract 25600 from both sides: $320x=169200 - 25600$.
$320x = 143600$.
Then divide both sides by 320: $x=\frac{143600}{320}=\frac{3590}{8}=\frac{1795}{4}=448.75$.

Answer:

$x = 448.75$