Question

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.

Answer 1

Here AB = 5cm,BC = 12cm, AC =13cm. 

AC² = AB² + BC² 

ΔABC is a right angled triangle at ∠B.

Area ΔABC = 1/2(BC x BA) 

= 1/2(12 x 5) 

= 1/2 x 60 

= 30cm² 

Also Area of ΔABC = 1/2 x AC x BD 

=1/2(13 x BD) 

30 = 1/2(13 x BD) 

13 X BD = 30 x 2 

BD = 60/13 

BD = 4.6 cm