If A is the area of a right angled triangle and b is one of the sides containing the right angle , then calculate the length of attitude on the hypotenuse?

Answer:

Let us consider

Area of the right angle = A

One side of the right angle = b

Area of the triangle A = 1/2 × b × h

h = 2A/b

Another side of the right-angled triangle containing the right angle (h) = 2A/b

According to Pythagoras theorem, the hypotenuse of the right-angled triangle is,

(Hypotenuse)²=(Base)²+(Height)²

(Hypotenuse)² = (b)² + (2A / b)²

⇒ (Hypotenuse)² = b² + (4A² / b²)

⇒ Hypotenuse = √[b² + (4A² / b²)

⇒ Hypotenuse = √[(b⁴ + 4A²) / b²

⇒ Hypotenuse = 1/b √[(b⁴ + 4A²)

According to Pythagoras theorem, area of the right angle is

A = 1/2 × 1/b √[(b⁴ + 4A²)] × altitude on hypotenuse (h)

⇒ 2A = 1/b √[(b⁴ + 4A²)] × h

⇒ 2Ab = √[(b⁴ + 4A²)] × h

⇒ h = 2Ab/√(b⁴ + 4A²)