Question

The sides of a triangle 5cm 12cm 13cm. Find the length of the perpendicular from the opposite vertex to the smallest side

Answer 1

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.

I hope it will help you..

Answer 2

a = 5cm, b =12cm, c= 13cm

s =(a + b + c)/2

= (5+ 12 + 13)/2 = 30/2

s = 15cm

Now apply Herons Formula


$\sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{15(15 - 5)(15 - 12)(15 - 13)}$

$\sqrt{15 \times 10 \times 3 \times 2}$

$\sqrt{5 \times 3 \times 5 \times 2 \times 3 \times 2}$

$= 30cm {}^{2}$

Area of triangle = 1/2 × b × h

30 = 1/2 × 5 × h

(30 × 2)/5 = h

12cm = h


Thanks