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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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First, verify the triangle is right-angled:
9^2 + 40^2 = 81 + 1600 = 1681 = 41^2
So it is a right triangle with legs 9 and 40, hypotenuse 41. The area...
A = \frac{1}{2} \times 9 \times 40 = 180 \text{ units}^2
The altitudes corresponding to each side are:
To side 9: \(h_9 = \frac{2A}{9} = \frac{360}{9} = 40\)
To side 40: \(h_{40} = \frac{2A}{40} = \frac{360}{40} = 9\)
To side 41: \(h_{41} = \frac{2A}{41} = \frac{360}{41} \approx 8.78\)
The shortest altitude is to the hypotenuse, which is:
\boxed{\frac{360}{41}}

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