Question

Suppose that a rectangle has a perimeter of 24 meters. Express the area A(x) of the rectangle in terms of the length x of one of its sides. A(x) = ??

Answer 1

`x-\ length\\\\y-\ width\\\\ A(x)=xy\\\\ Perimeter=2x+2y\\ 24=2x+2y\ \ \ |Subtract\ 2x\\ 24-2x=2y\ \ \ |Divide\ by\ 2\\ y=(24-2x)/(2)=12-x\\\\ A(x)=x(12-x)=12x-x^2\\\\ Area\ of\ rectngle\ can\ be\ expressed\ as\ A(x)=-x^2+12x`