the triangle below is isosceles. find the length of side $x$ in simplest radical form with a rational…
the triangle below is isosceles. find the length of side $x$ in simplest radical form with a rational denominator.
Answer
Explanation:
Step1: Identify equal sides
This is a right isosceles triangle, so the two legs are equal. The given leg length is 3, so the other leg is also 3.
Step2: Apply Pythagorean theorem
Use $a^2 + b^2 = c^2$, where $a=3$, $b=3$, $c=x$. $$x^2 = 3^2 + 3^2$$
Step3: Calculate the sum of squares
$$x^2 = 9 + 9 = 18$$
Step4: Solve for x and rationalize
Take the square root, then simplify the radical. $$x = \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$$
Answer:
$3\sqrt{2}$