How do I prove it is a diagonal?

[Zeroth]

Homework Statement

Inside of a square ABCD exists a point M such that |MA|=7 cm, |MB|=13 cm and |MC| = 17 cm. Calculate the area of the square

Homework Equations

The Attempt at a Solution

After a lot of formula searching I went and looked at the solution, there they proved that the point M i on the diagonal AC using the coordinate system and from there on it is easy to find the area. I need help in understanding the proof. They mentioned it is possible to do it using Pythagorean therorem but they didn't show how to do it and I don't see it. You can see my sketch in the picture. I know I am supposed to show my work and I have nothing to show, but can you at least give me some guidelines please?

 

[fresh_42]

Have you tried the law of sines to determine all relevant angles or some Pythagoras by drawing the heights of your triangles?
However, the first seems to be easier.

 

[Zeroth]

Is this enough?

 

[fresh_42]

Can't you type it in here? It's a) hard to read and b) skipped.

 

[Zeroth]

X/sin(γ) = 13/sin(α)

X/sin(δ)= 13/sin(β)

That is only possible if γ=δ and α=β

I hope the pic is understandable.

EDIT: Also.. I'm on the phone so it's a bit hard to write

 

[fresh_42]

What makes you think it is the diagonal? I guess you will have to determine the angles.

 

[ehild]

X/sin(γ) = 13/sin(α)

X/sin(δ)= 13/sin(β)

That is only possible if γ=δ and α=β

I hope the pic is understandable.

EDIT: Also.. I'm on the phone so it's a bit hard to write

It does not follow from your equations that γ=δ and α=β.

Look at the picture , apply Pythagoras' theorem and find x, y. (The red lines go through the point M and are parallel to the sides of the square. )

https://www.physicsforums.com/attachments/103906

 

[Zeroth]

I realized the problem with the angles later. With that picture I had no problem doing it. In the solutions was essentially the same thing but the coordinate system made it very confusing. Thank you very much

 

[SammyS]

Homework Statement

Inside of a square ABCD exists a point M such that |MA|=7 cm, |MB|=13 cm and |MC| = 17 cm. Calculate the area of the square

Homework Equations

The Attempt at a Solution

After a lot of formula searching I went and looked at the solution, there they proved that the point M is on the diagonal AC using the coordinate system and from there on it is easy to find the area. I need help in understanding the proof. They mentioned it is possible to do it using Pythagorean therorem but they didn't show how to do it and I don't see it. You can see my sketch in the picture. I know I am supposed to show my work and I have nothing to show, but can you at least give me some guidelines please?

If you take their word for it, that "the point M is on the diagonal AC", then the Law of cosines can be used to find the length of a side.

However, it's not too difficult to use the Pythagorean Theorem to show that M is on diagonal AC. From that finding the length of a side is easy.

Place point, P, along segment MC a distance 5 cm from M . What can you determine about triangle MPB ?

 

[Zeroth]

However, it's not too difficult to use the Pythagorean Theorem to show that M is on diagonal AC. From that finding the length of a side is easy.

Place point, P, along segment MC a distance 5 cm from M . What can you determine about triangle MPB ?

I will be completely honest with you. I ddon't see eye to eye with geometry. I can't determine anything.