Question

The lengths of sides of triangle are 5cm, 12cm, 13cm. Find the length of perpendicular from the opposite
vertex to the side whose length is 13cm?

Answer 1

Step-by-step explanation:

Let's say that the triangle is ABC with AB = 12, BC = 5, CA = 13.

Now you may see that triangle is right-angled at B, as AB² + BC² = CA².

And AB ⟂ BC with CA as hypotenuse and perpendicular's foot on CA be D.

Hence, ar(ABC) = ½  AB · BC = ½ CA · BD.

⇒ BD = ( AB · BC ) ÷ CA = ( 12 × 5 ) ÷ 13 = 60/13 cm.