Find the dimensions of a rectangle, length 7m less than three times the width and the area of the rectangle is 66m^2.

We know: length of a rectangle is 7m less than three times the width.

So let's set the length to l, width to w.

And we can get that l = 3w-7.

We also know that the area of the rectangle is 66 m^2.

Thus, l*w = 66.

So we have:

function 1: l=3w-7

function 2: l*w=66

plug function 1 to 2.

(3w-7) * w=66

3w^2-7w-66=0

w=6 and - 11/3.

And the width of a rectangle can not be negative.

So: w=6.

Plug w=6 back to function 1 or 2, either way is correct and can give you the length. In this case, I will plug it back to function 1.

l=3*6-7=11.

So: the width of the rectangle is 6, and the length of the rectangle is 11.