Question 641565
To solve, let's change the first two sentences into equations.  The first sentence says that the width of a rectangle is 8m less than the length.  In other words,

W = L - 8

The second sentence says that the area is {{{308m^2}}}.  The area of a rectangle is L x W (length times width).  So, in our second sentence, our equation would be

L x W = 308

Now, substitute L - 8 for the W in the second equation, and we will find our length:

L x (L - 8) = 308

Using the distributive property of multiplication, multiply L by (L - 8), which will give us:

{{{L^2 - 8L = 308}}}

If we subtract 308 from both sides of the equal sign, we will have a quadratic equation:

{{{L^2 - 8L - 308 = 0}}}

We can now solve for L by factoring, completing the square, or by using the quadratic formula.  Factoring is the easiest, so let's see if there are two numbers that when multiplied give us -308, and when added, give us -8:

1 x -308 = -308; 1 + -308 = -307  this won't work
-1 x 308 = -308; -1 + 308 = 307  this won't work

Let's try some bigger numbers.  How about 14 and 22?

-14 x 22 = -308; -14 + 22 = 8  this won't work
14 x -22 = -308; 14 + -22 = -8  this works!

We see that 14 and -22 work, so:

(L + 14)(L - 22) = -308, so

L = -14 and L = 22

Now, the length of a rectangle can never be a negative number, so -14 cannot be our length.  So, our length must be 22 meters

We know from the first sentence in our problem, that the width is 8m less than the length.  Since the length is 22, our width will be 8 less than that:

22 - 8 = 14

So, our width is 14m

FINAL ANSWER:  Length = 22m  and Width = 14m