1. **Problem Statement:** We are given a right triangle JKL with a right angle at K. A perpendicular KM is drawn from K to JL, creating two smaller right triangles JKM and KML. We know JK = 28 and JM = 17, and we need to find JL. 2. **Key Concept:** In a right triangle, when a perpendicular is drawn from the right angle vertex to the hypotenuse, it creates two smaller right triangles similar to the original triangle and to each other. This leads to the geometric mean relationships: $$ JK^2 = JM \times JL $$ This formula relates the leg JK, the segment JM on the hypotenuse, and the entire hypotenuse JL. 3. **Apply the formula:** Substitute the known values: $$ 28^2 = 17 \times JL $$ 4. **Calculate:** $$ 784 = 17 \times JL $$ Divide both sides by 17: $$ \frac{784}{\cancel{17}} = \frac{17 \times JL}{\cancel{17}} $$ $$ JL = \frac{784}{17} $$ 5. **Simplify:** $$ JL \approx 46.12 $$ 6. **Answer:** The length of JL is approximately 46.12 units.