In triangle PQR, PQ=13 , QR=14 , and PR=\(18\) . Let M be the midpoint of QR . Find PM.

Guest Jan 15, 2022

#1**0 **

so according to the Pythaogorean Thereom,

\(a^2+b^2=c^2\)

in this case,

\(7^2+{PM}^2=18^2\)

so \(49+PM^2=324\)

\(PM^2=275\)

\(PM=5\sqrt11\)

XxmathguyxX Jan 15, 2022

#2**0 **

I do not believe that the Pythagorean Theorem applies because PM is a median, not an altitude.

Since the triangle isn't an isosceles triangle, the median is not an altitude.

You can use this formula:

PM = sqrt( [ 2·PQ^{2} + 2·PR^{2} - QR ] / 4 )

geno3141 Jan 15, 2022

#3

#5**0 **

Hey, what's going on here? Someone doesn't like correct answers; that must be you, Melody.

Would you give me a reasonable explanation for blocking my answer?

civonamzuk
Jan 16, 2022

#6**0 **

Hey, what's going on here? Someone doesn't like correct answers; that must be you, Melody.

Would you give me a reasonable explanation for blocking my answer?

civonamzuk Jan 16, 2022

#7**0 **

It has already been answered.

You are just devaluing the good answer that has already been given.

All you are doing is encouraging cheating.

Melody
Jan 16, 2022

#8**0 **

Neither of the above answers is correct!!!

The correct answer is as follows:

PM = [sqrt(2 * 13^{2} + 2 * 18^{2} - 14^{2})] / 2

PM ≈ 14.053

~~~~~~~~~~~~~~~~~~~~~~~~~

Sides: a = 13 b = 18 c = 14

Area: T = 90.421

Perimeter: p = 45

Semiperimeter: s = 22.5

Angle ∠ A = α = 45.859° = 45°51'32″ = 0.8 rad

Angle ∠ B = β = 83.533° = 83°31'57″ = 1.458 rad

Angle ∠ C = γ = 50.609° = 50°36'31″ = 0.883 rad

Height: ha = 13.911

Height: hb = 10.047

Height: hc = 12.917

Median: ma = 14.756

Median: mb = 10.075

Median: mc = 14.053

civonamzuk
Jan 16, 2022

#14**0 **

Civonamzuk,

If you believe an answer is incorrect then it is up to you to state that clearly and politely.

If there is incorrect working or an incorrect statement then it is up to you to explain where the problem lies.

Just as Geno did when he explained why Xxmathman's answer was incorrect.

**Do not just over-write people with no explanation.**

Do not overwrite people without a clear explanation of why you are doing it.

Don't make a habit of giving final answers without explanations.

**Part done, well explained, unfinished answers are usually best! **

**Educators on this site want to aid learning, NOT facilitate cheating.**

Melody
Jan 17, 2022

#9

#11**-1 **

Your answer: PM = 5√11 = 16.58312395

Correct answer: PM = 14.05346932

civonamzuk
Jan 17, 2022

edited by
Guest
Jan 17, 2022

#10**+2 **

the midpoint of QR is M, so on eaither side of M, it is 7

one side is 7, one side is PM, and the hypotenuse is 18. So the pythagorean thereom works here

XxmathguyxX Jan 17, 2022