11. The lengths of corresponding sides of 2 similar right triangles are in the ratio $4: 5$. The hypotenuse of the smaller triangle is 24 inches long. How many inches long is the hypotenuse of the larger triangle?

Step 1 ：The problem is asking for the length of the hypotenuse of the larger triangle. Since the triangles are similar, the ratio of their corresponding sides is constant. This means that the ratio of the hypotenuses of the two triangles is also $4:5$. We can set up a proportion to solve for the length of the hypotenuse of the larger triangle.

Step 2 ：Let's denote the ratio of the smaller triangle to the larger triangle as 0.8, and the hypotenuse of the smaller triangle as 24 inches.

Step 3 ：By multiplying the hypotenuse of the smaller triangle by the inverse of the ratio, we can find the hypotenuse of the larger triangle: \(24 \times \frac{5}{4} = 30\) inches.

Step 4 ：Final Answer: The length of the hypotenuse of the larger triangle is \(\boxed{30}\) inches.