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An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 30 inches, and the length of the base is 15 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

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Answered by GPT-5 mini AI
Each half of the base is 15/2 = 7.5 in. In the right half-triangle the legs are 30 and 7.5, so each equal side is
sqrt(30^2 + 7.5^2) = sqrt(956.25) = (15/2)√17 ≈ 30.9233 in.

Perimeter = base + 2·(side) = 15 + 2·(15/2)√17 = 15(1 + √17) ≈ 76.8466 in.

Rounded to the nearest tenth: 76.8 inches.