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# Triangle

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

Jan 15, 2022

#1
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so according to the Pythaogorean Thereom,

$$a^2+b^2=c^2$$

in this case,

$$7^2+{PM}^2=18^2$$

so $$49+PM^2=324$$

$$PM^2=275$$

$$PM=5\sqrt11$$

Jan 15, 2022
#2
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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·PQ2 + 2·PR2 - QR ] / 4 )

Jan 15, 2022
#3
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PM = [sqrt(2 * 132 + 2 * 182 - 142)] / 2

PM ≈ 14.053

Jan 16, 2022
#4
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Why is that so? Is the problem because my answer is correct, or what?!

Guest Jan 16, 2022
#5
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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
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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?

Jan 16, 2022
#7
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You are just devaluing the good answer that has already been given.

All you are doing is encouraging cheating.

Melody  Jan 16, 2022
#8
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Neither of the above answers is correct!!!

The correct answer is as follows:

PM = [sqrt(2 * 132 + 2 * 182 - 142)] / 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
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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
edited by Melody  Jan 17, 2022
edited by Melody  Jan 17, 2022
#9
+360
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waitwaitwait

how am i wrong?

Jan 17, 2022
#11
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civonamzuk  Jan 17, 2022
edited by Guest  Jan 17, 2022
#13
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Civonamzuk,

All you have done is said "it is wrong because my answer is right and yours is different."   I have paraphrased

That must be the most useless answer of the day !

Melody  Jan 17, 2022
#10
+360
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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

Jan 17, 2022
#12
+1

Important: Triangles PQM and PRM are NOT right-angled triangles!!!

Guest Jan 17, 2022
#15
+117104
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Here is a scale drawing of the triangles.

There are obviously no right angles so Pythagoras's theorum cannot be used.

I hope that helps you xmathguy

Melody  Jan 17, 2022