<span> <span>Click here to see ALL problems on Geometry Word Problems<span><span>Question 503498: <span>a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the width of the pathway? </span> (Scroll Down for Answer!)</span>Did you know that Algebra.Com has hundreds of free volunteer tutors who help people with math homework? Anyone can ask a math question, and most questions get answers!<span>OR get immediate PAID help on:</span><span> Go!!!</span></span><span>Answer by </span>oberobic(2304) (Show Source):You can put this solution on YOUR website! <span>Borders are interesting because you have to remember that you have to pave the 4 corners. . The area of the garden = 12*16 = 192 square meters. . Then you add the border with width 'x'. So, Length is now L + 2x Width is now W + 2x . We are told: (L+2x)(W+2x) = 285 . (12+2x)(16+2x) = 285 . 192 +24x +32x +4x^2 = 285 . 4x^2 + 56x + 192 = 285 . 4x^2 + 56x - 93 = 0 . <span><span>Solved by pluggable solver: SOLVE quadratic equation with variable</span><span>Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=4624 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 1.5, -15.5. Here's your graph: </span></span> . You cannot have a negative width, so the border is 1.5 m. . Always check your work. L = 12 + 2(1.5) = 15 W = 16 + 2(1.5) = 19 15*19 = 285 Correct. . Answer: The border is 1.5 meters wide. . </span></span></span>
