Chapter 9.4, Problem 17PSB

To determine

To Calculate: The value of x

Answer to Problem 17PSB

The value of x is $\sqrt{5}$

Explanation of Solution

Given information:

ABC is a right-angled triangle.

Formula used:

Here, we are using Pythagoras theorem

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

Calculation:

  

Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  ${\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2$

  →${\left(AC\right)}^2=1+1$

  →$AC=\sqrt{2}$

Similarly, ${\left(AD\right)}^2=2+1$

  →$AD=\sqrt{3}$

And, $x^2=4+1$

  →$x=\sqrt{5}$

Conclusion: Hence,the value of x is $\sqrt{5}$