It is known that one of the legs of a triangle, similar to a right-angled triangle with legs 3m and 4m, is 27m. Find the legs of the second leg.

Given:
right-angled triangle ABC is similar to right-angled triangle A1B1C1,
1) AB = 3 meters,
AC = 4 meters,
A1B1 = 27 meters;
2) AB = 4 meters,
AC = 3 meters.
A1B1 = 27 meters.
Find the length of the leg A1C1 -?
Decision:
Consider similar right-angled triangles ABC and A1B1C1.
Therefore, their sides are proportional, that is, AB / A1B1 = AC / A1C1.
We get:
1) 3/27 = 4 / A1C1 (in order to find the unknown extreme term of the proportion, you need to divide the product of the middle terms of the proportion by the known extreme term);
A1C1 = (27 * 4) / 3;
A1C1 = 36 meters;
2) 4/27 = 3 / A1C1;
A1C1 = (27 * 3) / 4;
A1C1 = 20.25 meters.
Answer: 36 meters or 20.25 meters.