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

Question

30773 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-21T12:18:17

Below.

It is clear that the triangle is a right angled triangle.

Let AB=12 cm BC=5 cm and AC=13 cm

Now a perpendicular is drawn from A to AC.

#ar(ABC) = ½ AB · BC = ½ CA · BD.#

# BD = ( AB · BC ) / (CA #

Putting the respective values of the sides we get,

#BD=60/13# cm

You can also apply the heron's formula to get the answer to the question.

Answer 2 · 2018-07-21T13:21:15

#60/13#

The given side of triangle are #5, 12# & #13#.

The semi-perimeter #s# of given triangle with sides #a=5, b=12, c=13# is given as

#s=\frac{a+b+c}{2}#

#=\frac{5+12+13}{2}#

#=15#

Now, using Heron's formula, the area #\Delta# of given triangle is given as

#\Delta=\sqrt{s(s-a)(s-b)(s-c)}#

#=\sqrt{15(15-5)(15-12)(15-13)}#

#=30#

If #h# is the length of perpendicular to the side #c=13# drawn from opposite vertex then the area of given triangle

#\Delta=1/2(13)(h)#

#30=13/2 h#

#h=60/13#