The length of the second side of a triangle is twice the length of the first side. The length of the third side is 4 units more than the first side. The perimeter of the triangle is 52 units. How long is each side, and how do you determine that?

First side = 12 units

Second side = 24 units

Third side = 16 units

Step-by-step explanation:

First, we can assign variables for each side of the triangle to make it easier:

A = side 1

B = side 2

C = side 3

The length of the second side of the triangle is twice the length of the first side, so we know that B is twice the length of A. We can represent this in an equation like this:

B = A * 2

The length of the third side is 4 units more than the first side. This tells us that C is going to be 4 more than A:

C = A + 4

And finally, the perimeter of the triangle is 52 units. Since the perimeter is just all the sides added together, we can create this equation:

A + B + C = 52

To start solving for lengths, I'm going to plug in the first two equations we got into the third equation:

A + B + C = 52

A + (A * 2) + (A + 4) = 52

1A + 2A + 1A + 4 = 52

4A + 4 = 52

4A = 48

A = 12

Now that we know what A is, we can solve for the other two variables:

B = A * 2

B = 12 * 2

B = 24

C = A + 4

C = 12 + 4

C = 16

Now we have all three variables, just don't forget what the variables represent (first side, second side, third side).

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