Answer:
x = 3√2
Explanation:
You want the length x of the hypotenuse of an isosceles right triangle with sides of length 3.
Isosceles right triangle
The two legs of an isosceles right triangle are congruent. The length of the hypotenuse can be found from the Pythagorean theorem:
x² = 3² +3²
x² = 3²·2
x = √(3²·2) = 3√2
The length of side x is 3√2.
__
Additional comment
A isosceles right triangle is one of two "special" right triangles. The ratios of its side lengths are 1 : 1 : √2. This tells you the hypotenuse is √2 times the side length, as we found above.
The other "special" right triangle is the 30°-60°-90° triangle. Its side lengths have the ratios 1 : √3 : 2. Both of these are seen often in algebra, trig, and geometry problems.