Hello, dartanian24!
Code:
A
*
/|\
/ | \
/ | \
x / | \ x
/ |h \
/ | \
/ | \
B *-------*-------* C
½b D ½b
: - - - b - - - :
Let = base of the triangle.
Let = height of the triangle.
Then: .
In right triangle
Substitute [2]: .
Multiply by 4: .
Hence: .
We know that: .
Subnstitute [1] and [3]: .
Therefore: .
b) What is the domain of ? You probably mean "range".
The area has a minimum of 0 . . . when
The area is a maximum when the triangle is equilateral.
. . Then: .
. . The area is: .
The range is: .