Question

If 'a' be the area of a right triangle and 'b' one of the sides containing the right angle prove that the lengths of the altitude on the hypotenuse is
$2ab \div \sqrt{b {}^{4} + 4a ^{2} }$
please answer fast with explanation

no spam answers ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

d = 2ab /√( b²  + 4a²)

Step-by-step explanation:

'a' is  the area of a right triangle

'b' one of the sides containing the right angle

& Let c be another side containing the right angle

then Area = (1/2) * b * c  = a

=> c = 2a/b

h be hypotenuse  => h² = b² + c²

=> h² = b² + (2a/b)²   = b²  + 4a²/b²

=> h = √( b²  + 4a²)  / b

lengths of the altitude on the hypotenuse = d

Area of triangle  = (1/2) * h * d  = a

=> d = 2a/h

=> d  = 2a / (√( b²  + 4a²)  / b)

=> d = 2ab /√( b²  + 4a²)

QED

Proved