I am asked to set up a quadratic equations to solve some problems in my book. There were two problems I was not sure on how to go about setting up:
1. "The length of a rectangle is 4 meters more than twice its width. If the area of the rectangle is 126 square meters, find it's length and width."
I was able to find the answer (7 meters & 18 meters) by plugging in numbers that matched the conditions given. However, I don't see how I am supposed to have used the information given to set up a quadratic equation.
2. "A rectangular plot of ground measuring 12 meters by 20 meters is surrounded by a sidewalk of uniform width. The area of the sidewalk is 68 square meters. Find the width of the walk."
I do not see how to put this into the format of a quadratic equation. I tried to solve the answer in my own way, but came up with an incorrect answer.
I figured that since 12 times 20 is 240, 240 square meters would be the area of the rectangular plot of ground. The sidewalk surrounds the rectangular plot, and has an area of 68 square meters. I assumed this would mean that 68 square meters is the remainder of the length times width of the sidewalk subtracted by the area of the rectangular plot (240 square meters). Since 240+68=308, I took this to mean that the values for the length and width of the sidewalk multiplied together should equal 308. I found that if I increased the values of the length and width of the plot of land by two (yielding 14 and 22), I would have two numbers that multiply to 308 which could be the length and width of the sidewalk. Looking at this now, I can see that 14/22 is not proportional to 12/20, and so the sidewalk wouldn't exactly be "surrounding" the plot if it had such dimensions. I'm not sure where to go from here.
1. "The length of a rectangle is 4 meters more than twice its width. If the area of the rectangle is 126 square meters, find it's length and width."
I was able to find the answer (7 meters & 18 meters) by plugging in numbers that matched the conditions given. However, I don't see how I am supposed to have used the information given to set up a quadratic equation.
2. "A rectangular plot of ground measuring 12 meters by 20 meters is surrounded by a sidewalk of uniform width. The area of the sidewalk is 68 square meters. Find the width of the walk."
I do not see how to put this into the format of a quadratic equation. I tried to solve the answer in my own way, but came up with an incorrect answer.
I figured that since 12 times 20 is 240, 240 square meters would be the area of the rectangular plot of ground. The sidewalk surrounds the rectangular plot, and has an area of 68 square meters. I assumed this would mean that 68 square meters is the remainder of the length times width of the sidewalk subtracted by the area of the rectangular plot (240 square meters). Since 240+68=308, I took this to mean that the values for the length and width of the sidewalk multiplied together should equal 308. I found that if I increased the values of the length and width of the plot of land by two (yielding 14 and 22), I would have two numbers that multiply to 308 which could be the length and width of the sidewalk. Looking at this now, I can see that 14/22 is not proportional to 12/20, and so the sidewalk wouldn't exactly be "surrounding" the plot if it had such dimensions. I'm not sure where to go from here.
