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 $KT=16,KS=15\text{and S}U=\backslash \mathrm{grave}5$

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.

$KR=12,RT=4\text{and K}U=20$

Now,

$\begin{array}{l}KT=KR+RT\\ =12+4\\ \Rightarrow KT=16\end{array}$

And,

$\begin{array}{l}\frac{KR}{RT}=\frac{KS}{SU}\\ \Rightarrow \frac{12}{4}=\frac{KS}{KU-KS}\\ \Rightarrow 3=\frac{KS}{20-KS}\\ \Rightarrow 60-3KS=KS\\ \Rightarrow 4KS=60\\ \Rightarrow KS=15\end{array}$

And,

$\begin{array}{l}SU=KU-KS\\ =20-15\\ \Rightarrow SU=5\end{array}$

Therefore, the value of $KT=16,KS=15\text{and S}U=\backslash \mathrm{grave}5$