Question

I need help with this question

Answer 1

Answer:

  x = (3√2)/2

Step-by-step explanation:

In the isosceles right triangle the side lengths have the ratio ...

  1 : 1 : √2

This means the short leg (x) is 1/√2 times the length of the hypotenuse. You want the ratio with a rational denominator, so you need to multiply numerator and denominator by √2.

  $x=3\cdot\dfrac{1}{\sqrt{2}}=3\cdot\dfrac{\sqrt{2}}{(\sqrt{2})^2}\\\\\boxed{x=\dfrac{3}{2}\sqrt{2}}$