E is the midpoint of AC in right triangle ABC shown above. If the area of ΔABC is 24, what is the area of ΔBED?
A.
B.
C.
D.
E.
Choose the correct choice from the following options.
A) 9√3	B) 9√2	C) 12	D) 9	E) 6√2/3
Since BE is the median, Area of triangle ABE = Area of triangle EBC = 1/2 * Area of triangle ABC = 12.   Also, since Angle C = 45, AB = AC.   But, 1/2 * AB*AC = 24 =&gt; AC = \sqrt{48} = 4\sqrt{3}   AE = AC/2 = 2\sqrt{3}   Now, triangle EDC is again right angled. so area of triangle EDC = 1/2 * ED * DC .   But ED = DC and ED^2 + DC^2 = 12 =&gt; ED = \sqrt{6}   So area of triangle EDC = 1/2 *\sqrt{6} *\sqrt{6} = 3   Now area of triangle BCD = Area of triangle EBC - Area of triangle EDC =&gt; 12 -3= 
<gadget id="calculator">12 -3</gadget>
<output>9</output>
9.   ANSWER:9
<result>D</result>
E is the midpoint of AC in right triangle ABC shown above. If the area of ΔABC is 24, what is the area of ΔBED?
A.
B.
C.
D.
E.