Chapter 9.4, Problem 20PSB

To determine

To Calculate: The Perimeter of an isosceles right triangle.

Answer to Problem 20PSB

The Perimeter of an isosceles right triangle is $6\left(\sqrt{2}+1\right)$

Explanation of Solution

Given information:

Measure of hypotenuse is $6$ cm

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

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

In $\Delta ABC$

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

  →$36=x^2+x^2$

  →$\frac{36}{2}=x^2$

  →$x=3\sqrt{2}$

So that, Perimeter = $3\sqrt{2}+3\sqrt{2}+6$

  →$6(\sqrt{2}+1)$

Conclusion: Hence,the Perimeter of an isosceles right triangle is $6\left(\sqrt{2}+1\right)$