This is the solution for the Algebra plane geometric figure problem as asked by an anonymous visitor which read, "catrina and tom want to buy a rug for a room that s 14 by 15 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip if they buy a rug with an area of 110 square feet?"
It's easier to picture this. Draw a rectangle that's almost a square 14 x 15 feet. Within in draw another such figure but smaller. The space between that figure and the 14 x 15 figure is x. Now the smaller square has an area of 110 square feet. We now have an equation :
(15 -x ) (14 -x ) = 110
210 + x^2 -14x - 15x = 110
x^2 - 29x + 210 = 110
x^2 -29x + 100 = 0
(x - 25)(x - 4) = 0
x = 4 or 25 however using 25 would result in negative dimensions which does not make sense. So 4 is the answer
Check: (15 - 4) (14 - 4) = 110 = 11*10 = 110
Sunday, December 4, 2011
Plane Geometric Figure Problem 3 Solution
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Were do you get the 210 from?
ReplyDelete15 * 14 = 210
ReplyDelete(15 -x ) (14 -x ) = 110 <-- You are multiplying what's in the brackets together. 15*14 -x*14 -x*15 -x*-x = 210 - 14x - 15x + x^2 = x^2 - 29x + 210
wat is the unit of measure in the final answer?
ReplyDeleteft
ReplyDeleteWouldn't the strip be 2 since the length/width of the rug is 2x less than the room?
ReplyDeleteDidn't you skip a step? You went straight from (X^-29x + 100 = 0) to the quadratic equation of (x-25)(x-4)= 0. How do you reverse the simplification of a quadratic equation? In other words, how did you separate -29x into -25X and -4x?
ReplyDeleteI'm pretty confident you solved for the wrong unknown. You solved not for the width of the strip but for twice the width of the strip. You stated: "The space between that figure and the 14 x 15 figure is x." but if it is the case that x is the rugless border, then the problem to be solved is:
ReplyDelete(14-2x)(15-2x)=110
thus
210-58x+4x**2=110
4x**2-58x-100=0
x**2-(29/2)x-25=0
(x-2)(x-25/2)=0
so x=2 is the realistic answer if x is the rugless border.
The arithmetic works nicer your way, but in that case you have to say you are going to make x TWICE THE RUGLESS BORDER.
Ya I forgot to add the extra x -- its x on both sides of the width and length for the rug-- I will update. I just did it for one side in a hurry.
ReplyDeleteThanks for pointing that out...
ReplyDelete