Determine the length of the height of triangle ABC, that is perpendicular to BC, if BC= 15, AB=13 and AC=14.  

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We have the triangle ABC where :

AB = 13 AC = 14 and BC = 15

Then we can find the area usind the formula:

a =sqrt P(p-a)(p-b)(p-c)

Forst let us determine P

P = perimeter/2 = 13+14+15/2 = 42/2 = 21

==> a = sqrt(21*6*7*8) = 84

We...

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We have the triangle ABC where :

AB = 13 AC = 14 and BC = 15

Then we can find the area usind the formula:

a =sqrt P(p-a)(p-b)(p-c)

Forst let us determine P

P = perimeter/2 = 13+14+15/2 = 42/2 = 21

==> a = sqrt(21*6*7*8) = 84

We also know that:

area (a) = (1/2)* base*height

Since we need to determine the height of the perpindicular on BC, then let the height be AD and the base is BC.

==> a = (1/2)*AD*BC

==> 84= (1/2)*AD*15

==> AD = 84*2/15 = 56/5=11.2

Then AD = 11.2

 

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