Area of rectangle is 40m squared it has a length that is 2m less than 3 times its width what are the dimensions of retangle
lw=40
3w-2 = l
3w-2(w) = 40
you could honestly guess and get l = 10, w = 4
but expanding the previous equation we get 3w^2-2w= 40
3w^2-2w-40=0
We factor to get (x-4)(3x+10)
so, the width can be 4m, -10/3 m
but since it cant be negative, it must be positive.
plugging into the equation for l, we get
3w-2 = l
12-2 = l
l = 10
so, the dimensions are 10 x 4, which fits the guess.