Pythagorean Theorem

Question

ABCD is a kite, so AC ⊥ DB and DE=EB. Calculate the length of AC, to the nearest tenth of a centimeter.

Answer 1

Since DE = EB and DB is 6, DE = 3

By Pythagorean Theorem: CD^2 = CE^2 + ED^2 so 4^2 = CE^2 = 3^2, so CE = sqrt(7)

Also AE^2 + DE^2 = AD^2, so AE^2 + 3^2 = 7^2 and AE = sqrt(40)

AC = CE + AE = sqrt(7) + sqrt(40)