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

Find the surface-radius of earth, a) The distance d that can be seen fro...

a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950

Regrouping, in regrouping if we have abig number in the end what should i d...

in regrouping if we have abig number in the end what should i do?add an number on top of it,please help

Describe the sample of exponents , Describe the Sample of Exponents ? I...

Describe the Sample of Exponents ? Imagine, for example, that you are the P.E. coach at your school, and you need to divide one of your classes into teams. Your team has 45 stu

Describe visualize solutions of simultaneous equations, Describe Visualize ...

Describe Visualize Solutions of Simultaneous Equations ? By drawing the graph of each equation in a system of equations, you can see a picture of the system's solutions. Fo

Probability, Q)  In a lottery ,a person chooses six different natural numbe...

Q)  In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win

Descriptive statistics, Descriptive Statistics Statistics Definit...

Descriptive Statistics Statistics Definition of Statistics: it viewed as a subject is a process of tabulating, collecting and analyzing numerical data upon which importan

Finite population correction factor or fpcf), Finite Population Correction ...

Finite Population Correction Factor Or Fpcf) If a specified population is relatively of small size and sample size is more than 5 percent of the population then the standard er

Inverse tangent, Inverse Tangent : Following is the definition of the inve...

Inverse Tangent : Following is the definition of the inverse tangent.  y = tan -1 x     ⇔ tan y = x                     for            -∏/2 ≤ y ≤ ?/2 Again, we have a limi

Two consecutive integers is 15 find out the larger integer, If the differen...

If the difference among the squares of two consecutive integers is 15 find out the larger integer. Let x = the lesser integer and let x + 1 = the greater integer. The sentence,

Solve 4 cos(t )= 3 on[-8, Solve 4 cos(t )= 3 on[-8,10]. Solution : Here...

Solve 4 cos(t )= 3 on[-8,10]. Solution : Here the first step is identical to the problems in the previous section. First we need to isolate the cosine on one side by itself & t

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