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 $KR=27,KS=36\text{and S}U=12$.

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.

$RT=9,KT=36\text{and}KU=48$

Now,

$\begin{array}{l}KR=KT-RT\\ =36-9\\ \Rightarrow KR=27\end{array}$

And,

$\begin{array}{l}\frac{KR}{RT}=\frac{KS}{SU}\\ \Rightarrow \frac{27}{9}=\frac{KS}{KU-KS}\\ \Rightarrow 3=\frac{KS}{48-KS}\\ \Rightarrow 144-3KS=KS\\ \Rightarrow 4KS=144\\ \Rightarrow KS=36\end{array}$

And,

$\begin{array}{l}SU=KU-KS\\ =48-36\\ \Rightarrow SU=\text{'}12\end{array}$

Therefore, the value of $KR=27,KS=36\text{and S}U=12$.