BD is the hypotenuse of right triangle BED.
In right triangle BED, the legs are BE and ED.
BE = BA + AE
AB = 3; BC = 5
Use the Pythagorean theorem to find AC.
3^2 + (AC)^2 = 5^2
(AC)^2 = 25 - 9
AC = 4
ACDE is a square, so AE = AC = ED = 4
BE = BA + AE 3 + 4 = 7
Use the Pythagorean theorem to find the length of the hypotenuse, BD.
[tex] a^2 + b^2 = c^2 [/tex]
[tex] (BE)^2 + (ED)^2 = (BD)^2 [/tex]
[tex] 7^2 + 4^2 = (BD)^2 [/tex]
[tex] 49 + 16 = (BD)^2 [/tex]
[tex] (BD)^2 = 65 [/tex]
[tex] BD = \sqrt{65} [/tex]
