Find the following AE= DE= AD=.When the answer is not a whole number, leave a square root answer

Question

Consider rhombus ABCD with diagonals AC

 and DB. Suppose AC = 14 and DB = 8.

 Find the following. When the answer is not a whole number, leave a square root answer.

AE=

 DE=

 AD=

Answer 1

Diagonals of a parallelogram bisect each other.

AE = 1/2 of AC = 7

DE = 1/2 of DB = 4

Diagonal of a rhombus are perpendicular so AED forms a right triangle with AE and DE as legs and AD as hypotenuse.

By Pythagorean Theorem AE^2 + DE^2 = AD^2

so AD = sqrt(65)