Chapter 9.4, Problem 34PSD

To determine

To calculate: The length of a sideSR .

Answer to Problem 34PSD

The length of a SRis 12.48.

Explanation of Solution

Given information:

  $\overline{PR}\perp \overline{RT}$

Side $PT=25,$

Side $PR=15,$

Side $PS=ST+12.$

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

In right angled triangle PRT , we get

  $\begin{array}{l}{\left(15\right)}^2+{\left(RT\right)}^2={\left(25\right)}^2\\ {\left(RT\right)}^2=625-225\\ \therefore RT=\sqrt{400}\\ \therefore RT=20\end{array}$

  $IfST=x,SR=20-x$

In right angled triangle PRS , we get

  $\begin{array}{l}{\left(15\right)}^2+{\left(20-x\right)}^2={\left(x+12\right)}^2\\ 225+400-40x+x^2=x^2+24x+144\\ -64x=-481\\ \therefore x=\frac{481}{64}=7.51\\ SR=20-x\\ SR=20-7.51\\ SR=12.48\end{array}$