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$RT=8,KT=24\text{\hspace{0.17em}and\hspace{0.17em}}KS=20$.

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.

$KR=16,SU=10\text{\hspace{0.17em}and\hspace{0.17em}}KU=30$

Now,

$\begin{array}{l}\frac{KR}{RT}=\frac{KS}{SU}\\ \Rightarrow \frac{16}{KT-KR}=\frac{KU-SU}{10}\\ \Rightarrow \frac{16}{KT-16}=\frac{30-10}{10}\\ \Rightarrow 16=2KT-32\\ \Rightarrow 2KT=48\\ \Rightarrow KT=24\end{array}$

And,

$\begin{array}{l}RT=KT-KR\\ =24-16\\ \Rightarrow RT=8\end{array}$

And,

$\begin{array}{l}KS=KU-SU\\ =30-10\\ \Rightarrow KS=20\end{array}$

Therefore, The value of $RT=8,KT=24\text{\hspace{0.17em}and\hspace{0.17em}}KS=20$.