If A be the area of a right triangle and b one of the sides containing the right angle, the length of the altitude on the hypotenuse is__________.
a) 2A/√(b2+2A2) b) 2Ab/ √(b4+4A2) c)2Ab2/ √(b3+4A2) d)2A2b/ √(b4+3A2)
Let A be the area of the right triangle and b be one of the sides containing the right angle.
Let x be the length of the other leg
Let us observe the following figure.
Area of the triangle is
Thus,
Now apply Pythagorean Theorem.
Thus,
Area of the triangle ABC is
Hence (b) is the correct option.