Math Is Fun Forum

Henryhshsjaajja

Guest

Pythagoras question

I'm not entirely sure on my method to this question, but I want to see how you guys work it out, with an explanation please, I'm not entirely sure where I found the question but it is something like this.

A right angled triangle has sides A B C, with the right angle at angle BAC, the midpoint of BC is D.
DC is 3cm and BD is 6cm. Find the length of x where x is the distance from D to A.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Pythagoras question

Hi;

the midpoint of BC is D

If D is the midpoint of BC how can DB and DC be different lengths?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

MCKevinswift

Member

Registered: 2016-09-22

Posts: 1

Re: Pythagoras question

I've seen a similar question before, and he means that D is a point between B and C, such that it looks something like this.

[I have included the image in your post - bobbym]

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Pythagoras question

It is not possible to determine x;I should say data insufficient. If we draw a semicircle with BC as diameter point A will lie anywhere on this semicircle and will have a distance of 4.5 from M the midpoint of BC. So AD will have different values depending on location of A on the semicircle.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Pythagoras question

Hi;

If you want a single numerical answer then you will need to provide more information. Have you copied the entire question?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

MathsDhruv

Member

Registered: 2016-09-23

Posts: 1

Re: Pythagoras question

I have seen this type of question but in it AD was the median if it is the median then
in triangle ABC
(AB)²+(AC)²=(BC)²=81
in triangle ACD
angle ADC is 90 degree as AD is median
x²+36=(AC)²   x²=(AC)²-36
and similarly triangle ABD
x²+9=(AB)²    x²=(AB)²-9
(AB)²=(AC)²-36+9=(AC)²-27
(AB)²-(AC)²=-27
(AB)²+(AC)²=81
adding equations
2(AB)²=81-27
AB=3√3
x=3√2

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Pythagoras question

What I am saying is that more information is needed. The way the problem is stated there are an infinite number of solutions.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Pythagoras question

I have seen this type of question but in it AD was the median if it is the median then
in triangle ABC
(AB)²+(AC)²=(BC)²=81
in triangle ACD
angle ADC is 90 degree as AD is median
x²+36=(AC)²   x²=(AC)²-36
and similarly triangle ABD
x²+9=(AB)²    x²=(AB)²-9
(AB)²=(AC)²-36+9=(AC)²-27
(AB)²-(AC)²=-27
(AB)²+(AC)²=81
adding equations
2(AB)²=81-27
AB=3√3
x=3√2

I think you are considering AD as altitude, not a median.
If AD is altitude AD^2=BD*CD which gives the result quickly.This was derived considering similar triangles but a problem set on Pythagoras theorem has to be done accordingly.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}