sat suite question viewer

Choice B is correct. A rectangle’s diagonal divides a rectangle into two congruent right triangles, where the diagonal is the hypotenuse of both triangles. It’s given that the length of the diagonal is $5\sqrt{17}$ and the length of the rectangle’s shorter side is $5$. Therefore, each of the two right triangles formed by the rectangle’s diagonal has a hypotenuse with length $5\sqrt{17}$, and a shorter leg with length $5$. To calculate the length of the longer leg of each right triangle, the Pythagorean theorem, $a^2+b^2=c^2$, can be used, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse of the triangle. Substituting $5$ for $a$ and $5\sqrt{17}$ for $c$ in the equation $a^2+b^2=c^2$  yields $5^2+b^2={\left(5\sqrt{17}\right)}^2$, which is equivalent to $25+b^2=25\left(17\right)$, or $25+b^2=425$. Subtracting $25$ from each side of this equation yields $b^2=400$. Taking the positive square root of each side of this equation yields $b=20$. Therefore, the length of the longer leg of each right triangle formed by the diagonal of the rectangle is $20$. It follows that the length of the rectangle’s longer side is $20$.

Choice A is incorrect and may result from dividing the length of the rectangle’s diagonal by the length of the rectangle’s shorter side, rather than substituting these values into the Pythagorean theorem.

Choice C is incorrect and may result from using the length of the rectangle’s diagonal as the length of a leg of the right triangle, rather than the length of the hypotenuse.

Choice D is incorrect. This is the square of the length of the rectangle’s longer side.