An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options.–2 in.0 in.0.5 in.2 in.7.9 in.
The equal sides have total length 15.7 − b, so the triangle inequality requires 15.7 − b > b. Solving gives b < 7.85, and a side length must also be positive, so b > 0. Thus 0.5 in. and 2 in. are possible; 7.9 in. is too long, and −2 in. and 0 in. cannot be side lengths.
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