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

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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#