SOLUTION: The perimeter of a rectangle is 210 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 2250 square feet. Your answer should be one inter

Algebra ->  Inequalities -> SOLUTION: The perimeter of a rectangle is 210 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 2250 square feet. Your answer should be one inter      Log On


   

Question 1018971: The perimeter of a rectangle is 210 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 2250 square feet.
Your answer should be one interval in each box.
ANSWER: The length (in feet) of a side is in the interval....
or in the interval....

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
w and L, dimensions;
system%28wL%3C=2250%2C2w%2B2L=210%29

system%28wL%3C=2250%2Cw%2BL=105%29

w=105-L
-
%28105-L%29L%3C=2250
105L-L%5E2%3C=2250
-L%5E2%2B105L-2250%3C=0
L%5E2-105L%2B2250%3E=0

Check around the critical values L as %28105%2B-+45%29%2F2, or 30 and 75.
highlight_green%28%28L-30%29%28L-75%29%3E=0%29;
You cannot use L=0.
(0,30] ?
[30,75]?
[75,infinity) ?
Which interval will work?

RESULT: Only the first listed interval will work.
highlight%280%3CL%3C=30%29