Chapter 9.3, Problem 14PSB

To determine

To find: The length of side $BC$

Answer to Problem 14PSB

The length of side $BC$ = 12 m

Explanation of Solution

Given information :

  $BD=6\text{m}$ , $AB=\text{ 3 m}$ and $\angle DBC=\angle DBA={90}^{\text{o}}$

Formula used :

Use Pythagoras theorem

Calculation :

In $\Delta DBC$ ,

  $\begin{array}{l}\angle DBC={90}^{\text{o}}\\ DB=6\text{m}\\ \text{and }AB=3\text{m}\end{array}$

As per figure, if a perpendicular is drown to the hypotenuse of a right angle triangle. Then,

  $h^2=x\times y$

Here, $h=$ height of the perpendicular, $x=\text{length of }BC\text{ and }y=\text{length of }AB$ .

So,

  $\begin{array}{l}{6}^2=x\times 3\\ \Rightarrow x=\frac{36}{3}\\ \Rightarrow x=12\text{m}\end{array}$

Then, obviously, $BC=12\text{ m}$

Because sides of a right angle triangle are found in ratio of 3: 4: 5.