Question

Find the length of side xx in simplest radical form with a rational denominator.

Answer 1

`x = (√(22))/(2)`

Step by step explanation:

`\text{This is an isosceles right triangle}~ \left(45^(\circ) - 45^(\circ) - 90^(\circ)\right).\\\\\text{Apply Pythagorean theorem,}\\\\~~~~~~\left(√(11)\right)^2 =x^2 +x^2 \\\\\implies 11 = 2x^2 \\\\\implies x^2 = \frac{11}2\\\\\implies x = \sqrt{(11)/(2)}\\\\\implies x = (√(11))/(\sqrt 2)\\\\\implies x = (√(11)\sqrt 2)/(2)\\\\\implies x = (√(22))/(2)`