Question 641565: The width of a rectangle is 8m less them the length. The area is 308^2m. Solve for width and the length.
Please help
Thank you
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! 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  . 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:
If we subtract 308 from both sides of the equal sign, we will have a quadratic equation:
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
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