SOLUTION: I have a rectangular pen with an area of 2400 square meters. I remember that the width of the pen is 20 meters greater than the length. Find the length and width of the rectangular

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have a rectangular pen with an area of 2400 square meters. I remember that the width of the pen is 20 meters greater than the length. Find the length and width of the rectangular      Log On


   



Question 111796: I have a rectangular pen with an area of 2400 square meters. I remember that the width of the pen is 20 meters greater than the length. Find the length and width of the rectangular pen. I used the formula Let w = the width; Let w + 3 = the length; Area = lw and the instructor said that it was not a proper function because it only contained one variable. What am I doing wrong?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if the width of the pen is 20 meters greater than the length, you can't have w + 3 = the length;
you need to write:
the width=+W of the pen is 20+m+ greater than the +length=+L…....=> W=+L+%2B+20m
+A+=+2400++m%5E2

+A+=+W+L++…..substitute W and A
+2400++m%5E2+=+%28L+%2B+20m%29++L++
+2400++m%5E2+=+L%5E2+%2B+L20m+++………move 2400++m%5E2+++ to the right
+0+=+L%5E2+%2B+L20m++-+2400++m%5E2++………
Use quadratic formula to find only positive value for the length L
L%5B1%5D=%28-20+%2B+sqrt+%2820%5E2+-4%2A1%2A%28-2400%29+%29%29+%2F+%282%2A1%29
L%5B1%5D=%28-20+%2B+sqrt+%28400%5E2+%2B+9600%29%29+%2F+2
L%5B1%5D=%28-20+%2B+sqrt+%2810000%29%29+%2F+2
L%5B1%5D=%28-20+%2B+100%29+%2F+2
L%5B1%5D=+80+%2F+2

L%5B1%5D=+40m…….the length
Now find the width
W=+L+%2B+20m
W=+40m%2B+20m
W=+60m
Check:
+A+=+W+%2AL++…..
+A+=+40m+%2A+60m++…..
+A+=+2400m+%5E2+…..