ABC has a right angle at B. AC = 60, AE = 52 and CD = 39. Find the length of DE.
+128474 Strictly by "educated guessing"
Let us assume that right triangle ABC is a Pythagorean multiple of a 3 - 4 - 5 right triangle such that
BC = 36
AB = 48
AC = 60
And let us assume that right triangle DBC is a Pythagorean multiple of a 5 -12- 13 right triangle such that
DB = 15
BC = 36
DC = 39
Then BE = √ [AE^2 - AB^2] = √ [ 52^2 - 48^2] = √400 = 20
So
DE = √[ DB^2 + BE^2 ] = √ [ 15^2 + 20^2 ] = √ 625 = 25
Here is the image to show that this is true :
