Final answer:
Without the specific ratio between sides of the similar triangles or additional measurements, it is impossible to determine the length of the shorter leg of triangle rst from the given information. The Pythagorean theorem could help if more data was provided.
Step-by-step explanation:
The student has presented a problem regarding similar right triangles, specifically asking for the length of the shorter leg of one triangle, given the length of the longer leg of the other similar triangle.
Step-by-step Explanation
Since the two triangles are similar right triangles, the ratios of the corresponding sides are equal. We use the information given to write down the proportion, and then solve for the missing length assuming that the triangles' sides are proportional. Unfortunately, without the precise ratios or additional measures of sides from the triangles given in the question, we cannot determine the exact length of the shorter leg of triangle rst.
However, if we apply the Pythagorean theorem to the right triangle uvw with the longer leg being 42 inches, we could find the hypotenuse if the length of the other leg was known. Similarly, we would set up an equation to solve for the other leg. For example:
- If side a is the shorter leg and side b is the 42-inch longer leg, the theorem tells us that a² + 42² = hypotenuse².
- Once you have the hypotenuse or the ratio between the sides of the similar triangles, you would set up a proportion to solve for the missing side of triangle rst.
Without additional information, the question cannot be answered with the choices provided.