Prove that the length of the altitude on the hypotenuse, Mathematics

Assignment Help:

If A be the area of a right triangle and b one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2 Ab /√ b4+4A2.

1300_triangel 4.png

Ans:    Let QR = b

A = Ar(ΔPQR)

A = 1/2 x b x PQ

PQ = 2A/b ...........................(1)

Δ PNQ ∼ ΔPQR (AA)

⇒  PQ/PR = NQ/QR .....................(2)

From Δ PQR

PQ2 + QR2 = PR2

4A2/ b2 + b2 = PR2

1649_PR.png

Equation (2) becomes

2 A/bxPR  = NQ/b

NQ = 2A/PR

NQ = 2 A/√4 A2 + b4


Related Discussions:- Prove that the length of the altitude on the hypotenuse

Asymtotes, vwertical and horizontal

vwertical and horizontal

Minimum value of the function, How the property AM>or = GM used to get min...

How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a

Determine the property of partial ordered relation, Determine the property ...

Determine the property of Partial ordered relation Question: Partial ordered relation is transitive, reflexive and  Answer: antisymmetric

Geometry, can i get some triangle congruence proofs help?

can i get some triangle congruence proofs help?

Triangles, ABCD is a parallelogram which AB and CD are divides by P and Q. ...

ABCD is a parallelogram which AB and CD are divides by P and Q. Such that AP:PB=3:2 and CQ:QD=4:1. If PQ and AC are meet at R, show that AR=3/7AC.

Addition, #questiowhat is 1+1n..

#questiowhat is 1+1n..

Quadrilateral, similarities between rectangle & parallelogram

similarities between rectangle & parallelogram

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd