Prove that three times the sum of the squares, Mathematics

Assignment Help:

Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

Ans:    To prove 3(AB2 + BC2 + CA2) = 4 (AD2+ BE2 + CF2)

In any triangle sum of squares of any two sides is equal to twice the square of half of third side, together with twice the square of median bisecting it.

1619_triangle1.png

If AD is the median

AB2 + AC2 = 2 { AD2  + BC2/4}

2(AB2 + AC2) = 4AD2 + BC2

Similarly by taking BE & CF as medians we get

⇒ 2 (AB2 + BC2) = 4BE2 + AC2

& 2 (AC2 + BC2) = 4CF2 + AB2

Adding we get

⇒ 3(AB2 + BC2 + AC2) = 4 (AD2+ BE2 + CF2)


Related Discussions:- Prove that three times the sum of the squares

Differential equation - maple, 1. Consider the following differential equat...

1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t

What were her sales for the month of may of medical supplies, Kim is a medi...

Kim is a medical supplies salesperson. Each month she receives a 5% commission on all her sales of medical supplies up to $20,000 and 8.5% on her total sales over $20,000. Her tota

Trigonometry, Ashow that sec^2x+cosec^2x cannot be less than 4

Ashow that sec^2x+cosec^2x cannot be less than 4

Logs, log4^(x+2)=log4^8

log4^(x+2)=log4^8

Gauss-siedel or newton-rapson method, A one-line diagram of a simple three-...

A one-line diagram of a simple three-bus power system is shown in Figure 1 with generation at bus 1. The magnitude of voltage at bus 1 is adjusted to 1.05 per unit. The scheduled l

Function expansion, The functions {sinmx; cosmx}; m = 0,....∞ form a ...

The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these

Square numbers, determine the square of the following numbers ... a.8 b.13 ...

determine the square of the following numbers ... a.8 b.13 c.17 and d.80

Vector addition, Is it possible to add two vectors of unequal magnitude and...

Is it possible to add two vectors of unequal magnitude and get a resultant of zero?Please explain also. Ans) no it is not possible as .. if the magnitude is diffrent then they c

Limit, limit x APProaches infinity (1+1/x)x=e

limit x APProaches infinity (1+1/x)x=e

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