To solve this problem, we are going to set up a system of equations, or two equations that we can use to find out two variables. Let x represent the measure of one of the side lengths, and b represent the length of the base.
We know that the sum of the two equal legs is six more than three times the length of the length of the base, or the following equation.
2x = 6 + 3b
We also know that the perimeter, or the addition of both equal side lengths and the base equals 38, or the following equation.
2x + b = 38
To solve this system of equations, we can use substitution for 2x. (This means that because we know what 2x equals in terms of b, we can substitute this value into the other equation).
6 + 3b + b = 38
Now, we have to simplify and solve this equation.
4b + 6 = 38
4b = 32
b = 8
This means that the base measures 8 cm. Because we know this measurement, we can substitute 8 into one of our beginning equations for b to solve for x.
2x + b = 38
2x + 8 = 38
2x = 30
x = 15
Therefore, the base of the triangle is 8 cm, and the equivalent side lengths both measure 15 cm.
