A certain triangle has two angles that have the same measure. If the lengths of two sides of the triangle are 50 and 30, what is the least possible value for the perimeter of the triangle?

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The College Board loves isosceles triangles, and if you didn't recognize this as that type of problem, you will after you finish the triangle skill packet whose link is given below.

We are told that two angles of the triangle are the same, making it isosceles. Whenever you have a triangle with two angles the same, immediately extend the properties to include two sides being the same length. (The reverse of this is also true, of course. Whenever you are given two sides the same length, immediately extend the properties to include two angles being the same.)

If two sides of the triangle are the same, we can have a 50, 50, 30 triangle or a 30, 30, 50 triangle. The second one gives the smallest perimeter, which by definition is the sum of the lengths of the sides of a triangle, so the answer you would enter into the grid is 110 (30 + 30 + 50).

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