Question

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

Answer 1

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.