Chapter 9.4, Problem 27PSC

To determine

To calculate: The length of asideKM .

Answer to Problem 27PSC

The length of a sideKM is 7 ft.

Explanation of Solution

Given information:

Side $JO=25,$

Side $MO=20,$

Side $JK=2PO.$

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:

  

Apply Pythagoras Theorem in triangle OMJ and PMK .

In right angled triangle OMJ , we get

  $\begin{array}{l}{\left(JM\right)}^2={\left(JO\right)}^2+{\left(MO\right)}^2\\ {\left(JM\right)}^2={\left(25\right)}^2-{\left(20\right)}^2\\ {\left(JM\right)}^2=225\\ \therefore JM=15\end{array}$

  $\begin{array}{l}PO=x,JK=2x\\ KM=15-2x\\ PM=20+x\end{array}$

In right angled triangle PMK , we get

  $\begin{array}{l}{\left(25\right)}^2={\left(20+x\right)}^2+{\left(15-2x\right)}^2\\ {625}^2=400+40x+x^2+225-60x+4x^2\\ 0=-20x+5x^2\\ 0=5x(x-4)\\ \therefore x=4\\ KM=15-2x\\ \therefore KM=15-2(4)\\ =15-8\\ KM=7\end{array}$