find distance from 4th corner, given distances from other 3

[arthurhernandez123]

the book says "A Student desk is 4ft, 8ft, 12 ft from the three corners of a rectangular room 10 feet by 14 feet. Find the distance from the desk to the fourth corner.

What i have is:

14^2 +10^2=c^2
196+100=c
296=c

and the square root of that is 17.2 =c. I drew a rectangular shape and drew a diagonal ine corner to corner and labled it 17.2 Thats all i have and im not sure i did it right

 

[tkhunny]

What is the size of the desk?

 

[arthurhernandez123]

the book just says "a student desk is 4ft, 8ft, 12 ft from the three corners there is no size of desk

 

[Denis]

Intent probably is:
rectangle ABCD with AB=14, BC=10;
point P is inside, such that PA=4, PB=8, PC=12, PD= ?

Generel case formula(a=PA,b=PB,c=PC,d=PD) =:
d = sqrt(a^2 + c^2 - b^2)

Now I wonder why the room's size is given...