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'A' is the area of a right angled triangle and 'b' is the side containing right angle. Prove that the length of Altitude/hypotenuse=2AB/√(b^4+4A^2) |
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Answer» Answer: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)]. Step-by-step explanation: |
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