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

Hypothesis testing of the difference between proportions, Hypothesis Testin...

Hypothesis Testing Of The Difference Between Proportions Illustration Ken industrial producer have manufacture a perfume termed as "fianchetto." In order to test its popul

Right- and left-handed limits , Right- and left-handed limits : Next, let'...

Right- and left-handed limits : Next, let's see precise definitions for the right- & left-handed limits. Definition   For the right-hand limit we say that, if for eve

MAT201, #There is a balance of $1,234 and this person receive a refund chec...

#There is a balance of $1,234 and this person receive a refund check in the amount of $25 with her paycheck that was deposited into her account for $1500 which made her balance $27

Whats this, how do you determine if a graph has direct variation

how do you determine if a graph has direct variation

Trigonometric Identities, How to sovle or prove whether an equation is a id...

How to sovle or prove whether an equation is a identity?

Derive expressions for the mean and variance, On each day t of n days, N cu...

On each day t of n days, N customers of a supermarket were sampled and the number Xt expressing dissatisfaction was recorded. The results suggested that there were good and bad day

Probability transition matrices or brand switching, Define the Probability ...

Define the Probability Transition Matrices or Brand switching.

Markov chain, The Video Club Martin rents movies at "regular price" andat ...

The Video Club Martin rents movies at "regular price" andat "half price". Usually if the films are regularly priced one day, they will be at regular price the next day with probab

Product rule (f g)' = f ' g + f g', Product Rule: (f g)′ = f ′ g + f g′ ...

Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved

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