Rectangle and Triangles

[AvgStudent]

ABCD is a rectangle with the following lengths: AP=40, BP=24, CP=60. Find the length of DP.
I found this interesting old thread that was unanswered. I don't think there's enough information to solve. Thoughts?

 

[Dr.Peterson]

ABCD is a rectangle with the following lengths: AP=40, BP=24, CP=60. Find the length of DP.
I found this interesting old thread that was unanswered. I don't think there's enough information to solve. Thoughts?
View attachment 30780

No, it's perfectly solvable.

Suppose B is at (0,0), P is at (x,y), D is at (w,h). Write equations for AP^2, BP^2, and CP^2, and combine them to form the expression for PD^2. The answer is even a nice number!

 

[AvgStudent]

No, it's perfectly solvable.

Suppose B is at (0,0), P is at (x,y), D is at (w,h). Write equations for AP^2, BP^2, and CP^2, and combine them to form the expression for PD^2. The answer is even a nice number!

Hi @Dr.Peterson, probably due to my lack of knowledge in geometry, I don't see a way to set a relationship between the lengths you mentioned. Can you provide a bit more hint like what theorem would I use?

 

[lev888]

Hi @Dr.Peterson, probably due to my lack of knowledge in geometry, I don't see a way to set a relationship between the lengths you mentioned. Can you provide a bit more hint like what theorem would I use?

Given coordinates of 2 points, what is the formula for the distance between them?

 

[blamocur]

No, it's perfectly solvable.

Suppose B is at (0,0), P is at (x,y), D is at (w,h). Write equations for AP^2, BP^2, and CP^2, and combine them to form the expression for PD^2. The answer is even a nice number!

Somewhat unexpected since there are 4 variables but only 3 equations. There must be a "more geometric" solution, but I can't think of any.

 

[lev888]

Somewhat unexpected since there are 4 variables but only 3 equations. There must be a "more geometric" solution, but I can't think of any.

I haven't solved it, but theoretically, you don't need to find w and h, you only need the sum of their squares.

 

[AvgStudent]

Given coordinates of 2 points, what is the formula for the distance between them?

Ah yes of course. My brain....

 

[Dr.Peterson]

Somewhat unexpected since there are 4 variables but only 3 equations. There must be a "more geometric" solution, but I can't think of any.

Spoiler

What is [imath]e^2+g^2[/imath] in terms of [imath]x,y,u,v[/imath]?

Do the same for [imath]f^2+h^2[/imath].