SOLUTION: the area of rectangular garden should be at least 250 square meters. If its length is 5 meters more than twice its width, find the range of the possible values for the lot's length

Algebra ->  Rectangles -> SOLUTION: the area of rectangular garden should be at least 250 square meters. If its length is 5 meters more than twice its width, find the range of the possible values for the lot's length      Log On


   

Question 1196634: the area of rectangular garden should be at least 250 square meters. If its length is 5 meters more than twice its width, find the range of the possible values for the lot's length and width.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since the area is to be AT LEAST 250 square meters, you want to find the length and width for which the area is EXACTLY 250 square meters; then any larger length and width will satisfy the conditions of the problem.

The problem can be solved quickly by trial and error; 10*250 = 250, and 25 is 5 more than twice 10. So the minimum width and length are 10 and 25 meters.

For a formal algebraic solution....

x = width
2x+5 = length
x%282x%2B5%29=250
2x%5E2%2B5x=250
2x%5E2%2B5x-250=0
%282x%2B25%29%28x-10%29=0
x=-25%2F2 or x=10

Obviously the negative solution makes no sense in the actual problem, so the solution is x = 10.

ANSWER: The width can be anything equal to or greater than 10 meters.