SOLUTION: If the length of a rectangle is 5m more than its width, find the all possible values for the length so that the area of the rectangle will be at least 500m²

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If the length of a rectangle is 5m more than its width, find the all possible values for the length so that the area of the rectangle will be at least 500m²      Log On


   

Question 1177999: If the length of a rectangle is 5m more than its width, find the all possible values for the length so that the area of the rectangle will be at least 500m²
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the length of a rectangle is 5m more than its width, find the all possible values for the length so that the area of the rectangle will be at least 500m²
if the length L of a rectangle is 5m more than its width W, we have
L=W%2B5
the area of the rectangle:
A=L%2AW
500=%28W%2B5%29%2AW
500=W%5E2%2B5W
W%5E2%2B5W-500=0....factor
W%5E2-20W%2B25W-500=0
%28W%5E2-20W%29%2B%2825W-500%29=0
W%28W-20%29%2B25%28W-20%29=0
%28W+-+20%29+%28W+%2B+25%29+=+0
so, take only positive solution W=20
then L=20%2B5->L=25

Answer by ikleyn(52916) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This problem is about solving inequality,
            but  @MathLover1  mistakenly solved an equation,  instead.

            So,  I  came to bring a valid solution. 



Let L be the length, in meters.

Then the width is  (L-5) meters.


The area of the rectangle is  L*(L-5) square meters.


They want you solve this inequality


    L*(L-5) >= 500.


It is equivalent to


    L^2 - 5L - 500 >= 0.


Factor the left side


    (L-25)*(L+20) >= 0.


The solution to this inequality is the union of two sets  { L | L <= -20 } U { L | L >= 25}.


Due to the physicals sense, the length can not be negative.


So, the solution to the problem is the set  { L | L >= 25 meters }.    ANSWER

Solved.