Answer:
Area of Rectangle = [tex]26x - 2x^3[/tex]
Step-by-step explanation:
Rectangle two vertices lie on x axis ; two vertices lie on parabola [tex]y = 13 - x^2[/tex].
Supposing coordinates of upper right vertex of rectangle are P = [tex]x , y[/tex]
Due to parabola symmetry, width of rectangle is twice the distance horizontal (X) axis distance between Y axis & point P.
Width of rectangle = [tex]2x[/tex]
Length of rectangle = [tex]y[/tex] ; [tex]y = 13 - x^2[/tex]
Area of Rectangle = Length x Width
= [tex]2x (y)[/tex]
= [tex]2x (13 - x^2)[/tex]
= [tex]26x - 2x^3[/tex]