Chapter 6.5, Problem 25E

To determine

To find:the value of ST .

Answer to Problem 25E

The value of ST is $15$ yards.

Explanation of Solution

Given information : from triangleprovided in the question, it is observed that

  $\begin{array}{l}SR=9yd\\ RV=8yd\\ VT=4yd\\ UT=5yd\end{array}$

Formula used: Pythagoras theorem

  $a^2+b^2=c^2$

Calculation : to find the value of ST use the Pythagoras theorem,

Let c is ST,

  $a^2+b^2=c^2$

  $a=9$

  $\begin{array}{l}b=8+4\\ b=12\end{array}$

Now substitute the value of a and b then square and add then root square,

  $\begin{array}{l}{\left(9\right)}^2+{\left(12\right)}^2=c^2\text{ [substitute a by 9 and b by 12]}\\ 81+144=c^2\text{ [square]}\\ c^2=225\text{ [add]}\\ c=15\text{ [square root]}\end{array}$

Hence,Thevalue of ST is $15$ yards.