The lengths of the sides of a triangle are 7 cm, 12 cm, 13 cm. Find the length of perpendicular from the opposite vertex to the side whose length is 12 cm.
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Suppose that the triangle is ABC with AB = 12, BC = 5, CA = 13. Presently you may see that triangle is correct calculated at B, as AB² + BC² = CA².
Also, AB ⟂ BC with CA as hypotenuse and opposite's foot on CA be D.
Henceforth, ar(ABC) = ½ AB • BC = ½ CA • BD. ⇒ BD = ( AB • BC ) ÷ CA = ( 12 × 5 ) ÷ 13 = 60/13 cm.
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