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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.
Solution
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
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