a rectangle has a perimeter of 46cm and an area of 120cm squared. find its dimensions by writing an equation and using the quadratic formula to solve it. Thanks!

Let length = l , width = bPerimeter = 2 (l +b)46= 2 (l +b)(l + b) = 23l*b = 120So l + 120/l = 23l^2 + 120 - 23l = 0l^2 -15l + 8l + 120 = 0(l-8) (l - 15) = l = 8 or 15i.e if l =8, w=15 and if l = 15, w = 8