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.

Since 2a + b = 15.7, the two equal sides together have length 15.7 − b. For a valid triangle, the base must be positive and shorter than the combined length of the equal sides, so 0 < b < 7.85. The choices 0.5 inches and 2 inches meet that condition; 0 and −2 are not positive lengths, and 7.9 is too long.

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