A 33 kilometer bicycle race course is designed in the shape of a triangle. The first leg of the race is 5 km shorter than the second, and the third leg is twice the first. Find the distance of each leg of the race.

If the 2nd is x, then we have

(x-5) + x + 2(x-5) = 33
x = 12

Now figure the legs.

Let's assume the second leg of the race is x km long.

According to the given information, the first leg of the race is 5 km shorter than the second. Therefore, the length of the first leg would be x - 5 km.

The third leg of the race is twice the length of the first leg. So, the length of the third leg would be 2(x - 5) km.

Now, we can find the total distance of the race by adding up the lengths of all three legs:

Total distance = first leg + second leg + third leg

33 km = (x - 5) km + x km + 2(x - 5) km

Simplifying the equation:

33 km = x - 5 km + x km + 2x - 10 km

33 km = 4x - 15 km

Add 15 km to both sides:

48 km = 4x

Divide both sides by 4:

x = 12 km

Therefore, the second leg of the race is 12 km long.

Using this value, we can find the lengths of the other two legs:

First leg = x - 5 = 12 km - 5 km = 7 km

Third leg = 2(x - 5) = 2(12 km - 5 km) = 2(7 km) = 14 km

So, the distance of each leg of the race is as follows:

First leg: 7 km
Second leg: 12 km
Third leg: 14 km

To solve this problem, we can assign variables to represent the lengths of the legs of the triangle.

Let's say:
- x represents the length of the first leg
- (x + 5) represents the length of the second leg (since it is 5 km longer than the first leg)
- 2x represents the length of the third leg (since it is twice the first leg)

The total distance of the race is 33 kilometers, so the sum of the lengths of all three legs should be equal to 33.

Now we can set up an equation:

x + (x + 5) + 2x = 33

Combining like terms, we have:

4x + 5 = 33

Subtracting 5 from both sides of the equation, we get:

4x = 28

Dividing both sides by 4, we find:

x = 7

So, the length of the first leg is 7 km, the length of the second leg is (7 + 5) = 12 km, and the length of the third leg is 2 * 7 = 14 km.