# ABC is an isosceles triangle with AB=AC=13cm and BC=10cm. Calculate the length of the perpendicular from A to BC.

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using the pythagorean theorem we get height perpendicular bisector is 12.

13^2 - 5^2 = 144 = 12^2 so side is 12 and it would be the altitude to BC

now we find the area which is 1/2 ( b ) ( h ) we got the height/altitude which is 12 when base is 10

so area will be

1/2 ( 12 ) ( 10 ) = 60

using AB as the base the perpendicular which is the height would be solved by

2 A / b = h

120 / 13 would be the altitude to BC

you could use heron's formula/ hero's formula if you want but it would be too tedious

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