In figure 2, AB=BC. If the area of triangle ABE is x, what is the area of triangle ACD?

A) x sqrt2
B) x sqrt3
C) 2x
D) 3x
E) 4x

Those are similar triangles: angle BEA is also 62º, angle A is the same in both triangles, so angles ABE and ACD are also the same.

So yeah, if AB = BC, then the bigger triangle’s sides are all twice the size of the smaller triangle’s. If that’s the case, then the area of the bigger triangle will be FOUR TIMES the area of the smaller one. Why? Well, here’s why.

If the area of the small triangle is \dfrac{1}{2}bh, then the area of the big triangle will be \dfrac{1}{2}(2b)(2h)=2bh. 2bh is four times bigger than \dfrac{1}{2}bh.

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