The two shortest sides of a right triangle are 10 inches and 24 inches long. What is the length of the shortest side of a similar right triangle whose two longest sides are 36 inches and 39 inches?

I don't know how to do this one. I'm lost

Each is a scaled version of the 5-12-13 right triangle.

No worries! I'll explain how to approach this problem step by step.

To solve this problem, we need to understand the concept of similar right triangles. Similar triangles have the same shape but can be of different sizes, meaning their corresponding sides are proportional.

Step 1: Identify the corresponding sides:
In the given right triangle, we have the two shortest sides with lengths of 10 inches and 24 inches. Let's call these sides a and b, respectively.

In the similar right triangle, we are asked to find the length of the shortest side, which we'll call c. We are also given the lengths of the two longest sides, 36 inches and 39 inches.

Step 2: Write the proportion:
Since the triangles are similar, we can set up a proportion using the corresponding sides:
a/b = c/36

Step 3: Solve for the unknown side:
Now we can solve for c by substituting the known values:
10/24 = c/36

Step 4: Simplify and solve:
To simplify the equation, we can cross-multiply:
10 * 36 = 24 * c
360 = 24c

To solve for c, divide both sides by 24:
c = 360/24
c = 15 inches

So, the length of the shortest side of the similar right triangle is 15 inches.