Miachel wants to double the area of his garden show below by increasing the length and width by the same amount. what will be the dimensions of his garden then? use a representation and equation to solve
we want x,y and k such that
(x+k)(y+k) = 2xy
xy+kx+ky+k^2 = 2xy
y = k(x+k)/(x-k)
So, there are lots of solutions, with varying dimensions.
x y k xy (x+k)(y+k)
2 3 1 6 12
3 10 2 30 60
and so on