SOLUTION: triangle ABC is isosceles with base AC. AB=3x+18, BC=5x+4, AC=2x+15, what is x?

Question 693757: triangle ABC is isosceles with base AC. AB=3x+18, BC=5x+4, AC=2x+15, what is x?
Answer by RedemptiveMath(80) (Show Source): You can put this solution on YOUR website!
Out of the three sides of a isosceles triangle, two of them are congruent. The two sides that are equal are the sides that are not the base of the triangle. The base is the non-diagonal side that is usually shown horizontally and at the bottom of the diagram. In this case, our base is AC. So, the other two sides, or what we call the legs of an isosceles triangle, are congruent. These sides are given to us as AB and BC. To find x, simply set AB and BC equal to each other (by definition of congruence):

AB ≅ BC
AB = BC
3x+18 = 5x+4
14 = 2x
2x = 14
x = 7.
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