Lines, angles, and triangles SAT question

The correct answer is $\frac{44}{3}$. It's given that in triangle $RST$, angle $T$ is a right angle. The area of a right triangle can be found using the formula $A=\frac{1}{2}{l}_1{l}_2$, where $A$ represents the area of the right triangle, $l_1$ represents the length of one leg of the triangle, and $l_2$ represents the length of the other leg of the triangle. In triangle $RST$, the two legs are $\overline{\mathrm{RT}}$ and $\overline{\mathrm{ST}}$. Therefore, if the length of $\overline{\mathrm{RT}}$ is $72$ and the area of triangle $RST$ is $792$, then $792=\frac{1}{2}(72)(ST)$, or $792=(36)(ST)$. Dividing both sides of this equation by $36$ yields $22=ST$. Therefore, the length of $\overline{\mathrm{ST}}$ is $22$. It's also given that point $L$ lies on $\overline{\mathrm{RS}}$, point $K$ lies on $\overline{\mathrm{ST}}$, and $\overline{\mathrm{LK}}$ is parallel to $\overline{\mathrm{RT}}$. It follows that angle $LKS$ is a right angle. Since triangles $RST$ and $LSK$ share angle $S$ and have right angles $T$ and $K$, respectively, triangles $RST$ and $LSK$ are similar triangles. Therefore, the ratio of the length of $\overline{\mathrm{RT}}$ to the length of $\overline{\mathrm{LK}}$ is equal to the ratio of the length of $\overline{\mathrm{ST}}$ to the length of $\overline{\mathrm{SK}}$. If the length of $\overline{\mathrm{RT}}$ is $72$ and the length of $\overline{\mathrm{LK}}$ is $24$, it follows that the ratio of the length of $\overline{\mathrm{RT}}$ to the length of $\overline{\mathrm{LK}}$ is $\frac{72}{24}$, or $3$, so the ratio of the length of $\overline{\mathrm{ST}}$ to the length of $\overline{\mathrm{SK}}$ is $3$. Therefore, $\frac{22}{SK}=3$. Multiplying both sides of this equation by $SK$ yields $22=(3)(SK)$. Dividing both sides of this equation by $3$ yields $\frac{22}{3}=SK$. Since the length of $\overline{\mathrm{ST}}$, $22$, is the sum of the length of $\overline{\mathrm{SK}}$, $\frac{22}{3}$, and the length of $\overline{\mathrm{KT}}$, it follows that the length of $\overline{\mathrm{KT}}$ is $22-\frac{22}{3}$, or $\frac{44}{3}$. Note that 44/3, 14.66, and 14.67 are examples of ways to enter a correct answer.