Side ray of ED in triangle AED is twice the length of ray CD in rectangle ABCD. How do the areas of rectangle ABCD and triangle AED compare. Explain?

Question

anonymous · Answer

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directrix · Answer

I think they are equal. My reasoning follows.

directrix · Answer

If ED = 2CD, then EC = CD. --> C is the midpoint of segment ED.

The area of triangle AED = 1/2 its base AD times its height ED = 1/2* AD * 2 CD.

That quantity equals AD*CD. 

AD*CD is also the area of the rectangle.

anonymous · Answer

yeah, they are equal. agree to directrix. .