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

Let, AB = 5cm, BC = 12 cm and AC = 13 cm. Then, AC² = AB² + BC². This proves that ΔABC is a right triangle, right angles at B. Let BD be the length of perpendicular from B on AC.

Now, Area ΔABC `=1/2(BCxxBA)`

`=1/2(12xx5)=30" cm"^2`

Also, Area of ΔABC `=1/2ACxxBD=1/2(13xxBD)`

`rArrBD=60/13`cm