Question

find the length of side $x$ to the nearest tenth.
image of a right isosceles triangle with one leg labeled 12 and the hypotenuse labeled $x$

Explanation:

Step1: Identify triangle type and sides

This is an isosceles right triangle, so the two legs are equal: each leg = 12. We need to find the hypotenuse $x$.

Step2: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $a,b$ are legs, $c$ is hypotenuse.
$$x^2 = 12^2 + 12^2$$

Step3: Calculate the sum of squares

$$x^2 = 144 + 144 = 288$$

Step4: Solve for x and round

$$x = \sqrt{288} = 12\sqrt{2} \approx 16.97$$
Round to the nearest tenth: $x \approx 17.0$

Answer:

17.0