# Isosceles triangle space

In the right hand panel choose a property of a set of isosceles triangles - constant area - constant perimeter - constant altitude/base GREEN line shows all the isosceles triangles with that area area corresponding to the large GREEN dot is shown in the left panel BLUE line shows all the isosceles triangles with that perimeter perimeter corresponding to the large BLUE dot is shown in the left panel YELLOW line shows all the isosceles triangles with that altitude/base ratio altitude/base ratio corresponding to the large YELLOW dot is shown in the left panel Drag the WHITE dot to set the value of the property you have chosen. Drag the colored dot (color depends on your choice of property) to generate of set of isosceles triangles with a constant value of that property. Can you explain the shapes of the curves in the {base, altitude} plane [right panel] ? Can you write an expression for Area as a function of base length for all three cases? Can you write an expression for Perimeter as a function of base length for all three cases? Can you write an expression for altitude/base ratio as a function of base length for all three cases?