SAT Question 379ffefb: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice B is correct. The Pythagorean theorem states that for a right triangle, $c^2=a^2+b^2$, where $c$ represents the length of the hypotenuse and $a$ and $b$ represent the lengths of the legs. It's given that a right triangle has legs with lengths of $11$ centimeters and $9$ centimeters. Substituting $11$ for $a$ and $9$ for $b$ in the formula $c^2=a^2+b^2$ yields $c^2=11^2+9^2$, which is equivalent to $c^2=121+81$, or $c^2=202$. Taking the square root of each side of this equation yields $c=\pm \sqrt{202}$. Since $c$ represents a length, $c$ must be positive. Therefore, the length of the triangle's hypotenuse, in centimeters, is $\sqrt{202}$.