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 $KR=20,RT=10\text{and S}U=14$.

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.

$KT=30,KS=28\text{and}KU=42$

Now,

$\begin{array}{l}SU=KU-KS\\ =42-28\\ \Rightarrow SU=14\end{array}$

And,

$\begin{array}{l}\frac{KR}{KT-KR}=\frac{28}{14}\\ \Rightarrow \frac{KR}{30-KR}=2\\ \Rightarrow KR=60-2KR\\ \Rightarrow 3KR=60\\ \Rightarrow KR=20\end{array}$

And,

$\begin{array}{l}RT=KT-KR\\ =30-20\\ \Rightarrow RT=10\end{array}$

Therefore, the value of $KR=20,RT=10\text{and S}U=14$.