Question

Find the height of the triangle if the base is 4cm
Area and hypotenuse not mentioned

Answer 1

Answer:

not possible

this question is wrong

Answer 2

Answer:

We can use a property of right angle triangle for solving this problem, which can be stated as follows,

A right angle triangle with fixed hypotenuse attains

maximum area, when it is isosceles i.e. both height

and base becomes equal so if hypotenuse if H, then

by pythagorean theorem,

Base2 + Height2 = H2

For maximum area both base and height should be equal,

b2 + b2 = H2

b = sqrt(H2/2)

Above is the length of base at which triangle attains

maximum area, given area must be less than this maximum

area, otherwise no such triangle will possible.

Now if given area is less than this maximum area, we can do a binary search for length of base, as increasing base will increases area, it is a monotonically increasing function where binary search can be applied easily.

In below code, a method is written for getting area of right angle triangle, recall that for right angle triangle area is ½*base*height and height can be calculated from base and hypotenuse using pythagorean theorem.