MathDB

As in the following diagram, square

ABCD

and square

CEFG

are placed side by side (i.e.

C

is between

B

and

E

and

G

is between

C

and

D

). If

CE = 14

AB > 14

, compute the minimal area of

\triangle AEG

. [asy] size(120); defaultpen(linewidth(0.7)+fontsize(10)); pair D2(real x, real y) { pair P = (x,y); dot(P,linewidth(3)); return P; } int big = 30, small = 14; filldraw((0,big)--(big+small,0)--(big,small)--cycle, rgb(0.9,0.5,0.5)); draw(scale(big)*unitsquare); draw(shift(big,0)*scale(small)*unitsquare); label("

A

",D2(0,big),NW); label("

B

",D2(0,0),SW); label("

C

",D2(big,0),SW); label("

D

",D2(big,big),N); label("

E

",D2(big+small,0),SE); label("

F

",D2(big+small,small),NE); label("

G

",D2(big,small),NE); [/asy]

Problem Statement