Hi Jessica,
If you have a simple closed curve with perimeter p units and enclosing an area A square units then the isoperimetric quotient of this curve is
^{4 A} /_{p2}
Suppose that the curve is an isosceles triangle with side lengths a, a and b as in the diagram below.
The perimeter of this triangle is p = 2a + b and the area is A = ^{b}/_{2} h. The triangle PSR is a right triangle with hypotenuse of length a and sides of length h and ^{b}/_{2} . Use Pythagoras to express h in terms of a and b and substitute into the expression for A. Finally substitute these values for p and A into the expression for the isoperimetric quotient.
Penny
