A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is 13 cm.

Question

Philoid · Accepted Answer

Here AB=5cm,BC=12cm, AC=13cm.

AC2=AB²+BC²

ABC is a right angled triangle at ∠B.

Area ABC=1/2(BCxBA)

=1/2(12x5)

=1/2x60

=30cm²

Also Area of ABC=1/2xACxBD

=1/2(13xBD)

30=1/2(13xBD)

13XBD=30x2

BD=60/13

BD=4.6 cm