Question

For the figure shown, it is given that $\frac{KR}{RT}=\frac{KS}{SU}$. Copy and complete the table.

Short answer

The value of $KR=8,RT=4\text{and}KU=\backslash \mathrm{grave}15$.

Step-by-step solution

Step 1. Draw the given figure.

Step 2. Write down the given condition.

$\frac{KR}{RT}=\frac{KS}{SU}$

Step 3. Make the given table.

Step 4. From the table, write down the given values.

$KT=12,KS=10\text{and}SU=5$

Now,

$\begin{array}{l}\frac{KR}{RT}=\frac{KS}{SU}\\ \Rightarrow \frac{KR}{KT-KR}=\frac{10}{5}\\ \Rightarrow \frac{KR}{12-KR}=\frac{10}{5}\\ \Rightarrow 5KR=120-10KR\\ \Rightarrow 15KR=120\\ \Rightarrow KR=8\end{array}$

And,

$\begin{array}{l}RT=KT-KR\\ =12-8\\ \Rightarrow RT=4\end{array}$

And,

$\begin{array}{l}KU=KS+SU\\ =10+5\\ \Rightarrow KU=15\end{array}$

Therefore, the value of $KR=8,RT=4\text{and}KU=\backslash \mathrm{grave}15$.