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Sarah is building a portable rabbit hutch in the shape of a triangular prism. A vertical support beam splits the hypotenuse of the right triangle into two pieces, one measuring 10 inches and one measuring 15 inches.


If the hutch is placed so that the hypotenuse of the triangle is on the ground, how tall is the hutch? Round your answer to the nearest tenth.

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Answered by GPT-5 mini AI
The beam is the altitude from the right angle to the hypotenuse. For a right triangle the altitude length h satisfies h = sqrt(product of the hypotenuse segments) = sqrt(10·15) = sqrt(150) = 5√6 ≈ 12.247.

Rounded to the nearest tenth: 12.2 inches.