-

Question

-

directrix · Answer

Recall the 45-45-90 theorem.

directrix · Answer

Let x√2 be the side of the isosceles triangle on which the first regular pentagon is "built" and x be the length of the leg on which the second regular pentagon is constructed.

directrix · Answer

All regular pentagons are similar.
The scale factor of these two is this: x√2 to x which simplifies to √2 to 1.

directrix · Answer

Recall this theorem: If two polygons are similar, then the square of the scale factor of the two polygons is equal to the ratio of the areas of the two polygons.

@stupidinmath     What does this equal:  (√2/1)²  ?

That is the ratio of the areas.

If you post what you get, we can compare answers, okay?

anonymous · Answer

(√2/1)²
= 2

directrix · Answer

That is correct.   @stupidinmath

The area of the pentagon with the hypotenuse as a side is twice the area of the pentagon with the leg as a side.

anonymous · Answer

wai, how is it drawn? is it this way?
|dw:1385225331211:dw|