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

#algebra 2 .., encoded with the matrix -3 -7 and 4 9. what lights up a socc...

encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)

Explain adding rational expressions different denominators, Explain Adding ...

Explain Adding Rational Expressions with Different Denominators When you add or subtract fractions or rational expressions that have different denominators, you must first find

Solve the radical form, Simplify following. Suppose that x, y, & z are posi...

Simplify following. Suppose that x, y, & z are positive.                      √ y 7 Solution In this case the exponent (7) is larger than the index (2) and thus the fir

Complex roots - second order differential equations, We will be looking at ...

We will be looking at solutions to the differential equation, in this section ay′′ + by′ + cy = 0 Wherein roots of the characteristic equation, ar 2 + br + c = 0 Those

first and third quartiles, From the data given below calculate the value o...

From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles.

Please help me solve these Problems step by step, What angle (to the neares...

What angle (to the nearest degree) corresponds to the cos 0.6 or what is cos-1(0.6)? (Note: Use Appendix I) What angle (to the nearest degree) corresponds to the sin 0.6 or what

How much area will it irrigate in 30 minutes , Water in a canal 30 dm wide ...

Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?

theoretical minimum number of stations, A company is setting up an assembl...

A company is setting up an assembly line to produce 100 units/hour. The table shown below identifies the work elements, times, and immediate predecessors. a)      What cycle tim

Algebra, how do i sole linear epuation

how do i sole linear epuation

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