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

Fractions, Mr. And Mrs. samuel visited Florida and purchased 120 oranges. ...

Mr. And Mrs. samuel visited Florida and purchased 120 oranges. They gave 1/4 of them to relatives, ate 1/12 of them in the hotel, and gave 1/3 of them to friends. The shipped the

Calculate values of the derivative, First, see that the right hand side of ...

First, see that the right hand side of equation (2) is a polynomial and thus continuous. This implies that this can only change sign if this firstly goes by zero. Therefore, if the

Calculas, how to deal with integration by parts

how to deal with integration by parts

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

Describe least three characteristics at medieval world, Based upon the prim...

Based upon the primary sources, describe at least three characteristics that mark the early modern world as distinctly different than the Medieval world that preceded it. You might

Find the slope of this line, The following graph shows the growth of the me...

The following graph shows the growth of the median home value in a particular region of the United States starting in 1996.  The graphs starts in 1996 and shows the trend through t

Find out a if f(x) is continuous at x = -2 , Example   Given the graph of ...

Example   Given the graph of f(x), illustrated below, find out if f(x) is continuous at x = -2 , x = 0 , and x = 3 . Solution To give answer of the question for each

Matrix inverse, Here we need to see the inverse of a matrix. Provided a squ...

Here we need to see the inverse of a matrix. Provided a square matrix, A, of size n x n if we can get the other matrix of similar size, B that, AB = BA = I n after that we call

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