Math CentralQuandaries & Queries


Question from maris, a student:

Find the sides of a 30-60-90 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables.


Suppose the sides of the triangle are a, b and c units in length where a is the length of the short side and c is the length of the hypotenuse. You know that

a + b + c = 6.

Since it is a right triangle Pythagoras theorem gives you a second equation in a, b and c. The third equation you use depends on what you know about a 30-60-90 triangle. I know that the length of the hypotenuse is twice the length of the shortest side so that will give a third equation.

Solve the three equations for a, b and c and make sure you verify that the perimeter is 6.


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