MathDB

Square

ABCD

has side length

4

. Side

AB

is extended to point

E

so that

AE

has the same length as

AC

, as shown below. What is the length of

EC

? Express your answer as a decimal to the nearest hundredth. [asy] size(80); defaultpen(fontsize(8pt)); pair EE = (4sqrt(2),0); pair A = (0,0); pair B = (4,0); pair C = (4,4); pair D = (0,4); draw(A--B--C--D--cycle); draw(A--EE); draw(C--EE,dotted); label("

A

",A,SW); label("

B

",B,S); label("

C

",C,N); label("

D

",D,N); label("

E

",EE,S); [/asy]

Problem Statement