The sides of a triangle are 51 cm, 35 cm, and 26 cm. What is the length (in cm) of its altitude corresponding to the side with a length of 35 cm?
24
Using Heron's formula with sides 51, 35 and 26: semi-perimeter \(s=\dfrac{51+35+26}{2}=56\).
Area: \(\sqrt{56\times5\times21\times30} = \sqrt{176400} = 420\) cm2.
Altitude to the 35 cm side: \(\text{Area}=\dfrac12\times35\times h \Rightarrow h=\dfrac{2\times420}{35}=24\).
Hence, the altitude corresponding to the 35 cm side is 24 cm.
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