Official Guide - p. 260, q 9 -- triangle CDE

[baily106]

How would you approach the following?

It is question #9 on page 260.
Unfortunately, I cannot draw the image.
The question states, in the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG?

I understand that the area of a triangle is half of the base times the height. so for triangle CDE 42 is a result of dividing 84 by 2. How do you determine what the base and the height is? Then one multiplies it by 3 since there are three triangles to find the area of triangle ADG or is it something else?

Thanks,
Anisha

[tommywallach]

Hey Baily,

In this case, the triangles are similar, which means everything is expanding at the same rate. if AB = BC = CD, then DE = EF = FG. Also, BF = 2CE and AG = 3CE (because the bases are expanding in the same ratio of 1:2:3.

So the big height DG = 3DE and the big base AG = 3CE. This means that the final area will be 9 times as big as the area of CDE, so we just multiply 42 by 9.

Make sense?

-t

[baily106]

Yes, it does.
Thanks.

[tommywallach]

Yay!