Chapter 9.5, Problem 7PSA

To determine

To find: The length of side BC and side AD .

Answer to Problem 7PSA

The length of BC is 10 and AD is 4.5.

Explanation of Solution

Given information:

Side $DC=8,$

Side $BD=6.$

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:

  

To calculate side BC , we must apply Pythagoras Theorem.

In right angle triangle BDC , we get

  $\begin{array}{l}{\left(BD\right)}^2+{\left(DC\right)}^2={\left(BC\right)}^2\\ {\left(6\right)}^2+{\left(8\right)}^2={\left(BC\right)}^2\\ 36+46={\left(BC\right)}^2\\ 100={\left(BC\right)}^2\\ \therefore BC=10\end{array}$

Let, $AD=x$

So,

  $\begin{array}{l}\frac{8}{10}=\frac{10}{8+x}\\ 8(8+x)=100\\ 64+8x=100\\ 8x=36\\ \therefore x=\frac{36}{8}\\ AD=x=4.5\end{array}$