SAT Question 498d6795: 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 in triangle $ABC$, angle $B$ is a right angle. Therefore, triangle $ABC$ is a right triangle, where the hypotenuse is side $AC$ and the legs are sides $AB$ and $BC$. It's given that the lengths of sides $AB$ and $BC$ are $10\sqrt{37}$ and $24\sqrt{37}$, respectively. Substituting these values for $a$ and $b$ in the formula $c^2=a^2+b^2$ yields $c^2={\left(10\sqrt{37}\right)}^2+{\left(24\sqrt{37}\right)}^2$, which is equivalent to $c^2=100\left(37\right)+576\left(37\right)$, or $c^2=676\left(37\right)$. Taking the square root of both sides of this equation yields $c=\pm 26\sqrt{37}$. Since $c$ represents the length of the hypotenuse, side $AC$, $c$ must be positive. Therefore, the length of side $AC$ is $26\sqrt{37}$.