Question 23539: PLEASE HELP ME!! I don't know what i'm doing and i've been up all night trying to figure out these word problems! Please Help! Here is the problems: A garden plot 4 m by 12 m has one side along a fence. The area of the garden is to be doubled by digging a border of uniform width on the on the other three sides. What should the width of the border be?
Here is the other problem: Vanessa built a rectangular pen for her dogs. She used an outside wall of the garage for one of the sides of the pen. She had to buy 20 m of fencing in order to build the other sides of the pen. Find the dimenstion of the pen if its area is 48 m^2.
Help would be GREATLY appreciated. Thanks
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! #1) OK, first of all, it makes a difference which side of the garden is along the fence. After solving it, it worked better to have the 12m side along the fence, so that's what I'm going to assume. We know the garden is 4m x 12m, so the area is 48. We want this doubled, so we want an area of 96. Now, if you draw a picture, you can draw a border around the garden on the remaining 3 sides, and let the width of the border (the distance between the edge of the garden and the edge of the border) equal x. So, using those 3 lengths of x, we get the equation (12 +2x)(4+x)=96. Multiplying this out, we get a quadratic equation, and can solve for x, giving us the answer of x=2m.
#2) Again, we can draw a picture, and this time we don't know any of the sides' lengths, so we can say side x is next to the garage, and the other length is y. We want an area of 48 and a perimeter (minus x) of 20. So we can form the equations xy=48 and 2y+x=20. Then this system of equations can be solved for x and y to get x=4m and y=12m.
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