The sides of a triangle are 75 cm, 21 cm, and 72 cm. What is the length (in cm) of its altitude corresponding to the side with a length of 21 cm?
72
Check if the triangle is right-angled: \(21^2+72^2 = 441+5184=5625=75^2\), so it is right-angled with legs 21 and 72.
Area of the triangle: \(\tfrac12\times21\times72 = 756\) cm2.
Using area \(=\tfrac12\times21\times h\), the altitude to the side 21 is \(h=\dfrac{2\times756}{21}=72\) cm.
Hence, the altitude corresponding to the side of length 21 cm is 72 cm.
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