Question

the triangle below is isosceles. find the length of side $x$ to the nearest tenth.
image of a right isosceles triangle with one leg labeled 11 and hypotenuse labeled $x$

Explanation:

Step1: Identify equal sides

This is a right isosceles triangle, so the two legs are equal. Both legs have length 11.

Step2: Apply Pythagorean theorem

Use $a^2 + b^2 = c^2$, where $a=b=11$, $c=x$.
$$x^2 = 11^2 + 11^2$$

Step3: Calculate the sum of squares

$$x^2 = 121 + 121 = 242$$

Step4: Solve for x

Take the square root of 242, then round to the nearest tenth.
$$x = \sqrt{242} \approx 15.6$$

Answer:

15.6