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 $KR=6,KT=8\text{\hspace{0.17em}and}SU=3$.

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.

$RT=2,KS=9\text{\hspace{0.17em}and}KU=12$

Now,

$\begin{array}{l}\frac{KR}{RT}=\frac{KS}{SU}\\ \Rightarrow \frac{KR}{2}=\frac{9}{KU-KS}\\ \Rightarrow \frac{KR}{2}=\frac{9}{12-9}\\ \Rightarrow KR=6\end{array}$

And,

$\begin{array}{l}KT=KR+RT\\ =6+2\\ \Rightarrow KT=8\end{array}$

And,

$\begin{array}{l}SU=KU-KS\\ =12-9\\ \Rightarrow SU=3\end{array}$

Therefore, the value of $KR=6,KT=8\text{\hspace{0.17em}and}SU=3$.