If in `Delta ABC, b = 3 cm, c = 4 cm` and the length of the perpendicular from A to the side BC is 2 cm, then how many such triangle are possible ?

Answer

two

Explanation

`CD = sqrt(3^(2) -2^(2)) = sqrt5`
`BD = sqrt(4^(2) -2^(2)) = 2sqrt3`
Now, area of `Delta ABC = (1)/(2).2. (sqrt5 + 2 sqrt3) = (1)/(2).4.3. sin A`
`rArr sin A = (sqrt5 + 2 sqrt3)/(6) lt 1`
Also, `a gt b, a gt c`
Hence, A can have two values