Square and Inscribed Equilateral Triangle
Given
square WXYX and equilateral triangle ABZ, find the ratio of the areas of
∆BYZ and ∆ABX.
Let the sides of the
equilateral triangle each be of
length c and let the side of the
square be of length 1.
If we let the legs of isosceles right triangle ABX be of length, that
is BX = a and AX = a, then BY =
1-a.
The area of a right triangle is half the product of the legs so the ratio of
the areas of ∆BYZ and ∆ABX is
Hint? Or, how about a GSP sketch? If desperate, see one solution.
Extension/alternative:
Using geometry, show that
Area triangle AXB
= Area triangle AWZ +
Area triangle BYZ
Hint? See GSP Sketch.