Is it possible to build a fence on 3 sides of a rectangular piece of land with an area of 100m^2, so that the total length of the fence is 25 m ?
I created the two equations l+2w=25m (same as l=25-2w) and l*w=100m^2 . Then I put them together to make (25-2w)(w)=100 , and then I distribute the "w" and complete the square. The back of the book says it isn't possible though. Anyone able to do this and tell me what you get? Because I AM getting a final answer, but its not working out.
Well lets think of this in a different way!
lets find the max area that can be enclosed with 25 meters of fence.
we know that
subbing the 2nd equation into the first we get
if we complete the square on this we get
So the maximum area that can be enclosed is 78.125 square feet.
So the answer is no.
OH! Ok, now I see what I am not doing. When I see that 25/2 , I always assume that I already divided by 2, but i forget I have to divide by 2 again (mulitply 25/2 by 1/2) and THEN square.
Thanks! Took a bit of thinking to realize my error.
On a side note, I'm doing another question. I'm fairly confident that I can complete the square this time, no problems, but I can't figure out the equation to begin with!
The word problem:
The hypotenuse is 3 cm greater in length than the next longest side of a right triangle. The line perpendicular to THAT line is 3 cm shorter . What are the side lengths. (so, you have your hypotenusse, c, which is 3 cm longer than side b, which is 3 cm longer than side c )