Question

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Answer 1

Answer:

h = 2Ab/√b⁴ + 4A²

Step-by-step explanation:

Given:

Area of right angled triangle is 'A' and base is 'b'.

We know that Area of right angled triangle = (1/2) * base * height

⇒ A = (1/2) * b * h

⇒ 2A = b * h

⇒ h = 2A/b

By Pythagoras theorem,

Hypotenuse = √b² + h²

                    = √b² + (2A/b)²

                    = √b² + 4A²/b²

                    = √b⁴ + 4A²/b²

                    = (1/b)√b⁴ + 4A²

Now,

Area of triangle ABC is:

⇒ A = (1/2) * (1/b)√b⁴ + 4A² * h

⇒ 2Ab = √b⁴ + 4A² * h

⇒ h = (2Ab)/(√b⁴ + 4A²).

Hope it helps!

Answer 2

Step-by-step explanation:

Base of the right angled triangle is 'b' units.

Area of the right angled triangle is "A' sq units.

A = 1/2 × b × h

⇒ h = 2A / b

Another side of the right angled triangle containing the right angle = 2A / b

Hypotenuse of the right angled triangle according to Pythagoras theorem:

(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)]

Area of the right angle considering hypotenuse as the base.

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

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

2Ab = √[(b4 + 4A2)] × altitude on hypotenuse

Altitude on hypotenuse = 2Ab / √[(b4 + 4A2)]

Therefore, length of the altitude on hypotenuse of the right angled triangle is 2Ab / √[(b4 + 4A2)].