The two shortest sides of a right triangle are 10 in and 24 in long. What is the legnth if the shortest side of a similar triangle whose two longest sides are 36 in and 39 in?
10/24 = 5/12
so this is a 5, 12, 13 right triangle
39/13 = 3 (of course 26/12 is 3 also)
so
5*3 = 15
To solve this problem, we can use the concept of similarity of triangles. Similar triangles have proportional sides.
In the given right triangle, let's label the shortest side as a, and the other side as b. So we have a = 10 in and b = 24 in.
We are also given another similar triangle with two longest sides of 36 in and 39 in. Let's label the shortest side of this triangle as x.
To find the length of the shortest side of the similar triangle, we need to find the proportional length.
We can set up a proportion using the corresponding sides of the two triangles:
a/b = x/36
Now we can substitute the known values:
10/24 = x/36
To solve for x, we can cross-multiply:
10 * 36 = 24 * x
360 = 24x
Next, we can solve for x by dividing both sides of the equation by 24:
360/24 = x
15 = x
Therefore, the length of the shortest side of the similar triangle is 15 inches.