The rectangular playing area of a professional football field is 100 yards long. The perimeter of the playing?

Question

1. In the perimeter formula , l is the length and w is the width.



a. Name the variables in the formula.





b. Look at the problem. Which variables are known? Which are unknown?





c. Complete the sentence to describe the relationship between l, w, and P in words.



If you know l and w and want to find P, ________________________________

_________________________________________________________________.





Solution Method 1



2. Solve the literal equation for the unknown variable. Be sure to show all the steps.







3. Complete the sentence to describe the relationship between l, w, and P in words.



If you know l and P and want to find w, ________________________________

_________________________________________________________________.





4. Show how you can use the new literal equation to find the width. Be sure to show all the steps.







5. What is the width of the field?







Solution Method 2



6. Substitute the known information from the problem into the perimeter formula . Simplify where necessary. Then, solve the equation for the unknown variable. Be sure to show all the steps.









7. What is the width of the field?





Comparing Methods



8. Look back at the answers you found. The two methods should have produced the same answer. Which method did you prefer? Why? Explain your preference using at least three sentences.

Answer 1

Hi,



1. In the perimeter formula , l is the length and w is the width.



a. Name the variables in the formula.

p = perimeter

l = length

w = width



b. Look at the problem. Which variables are known? Which are unknown?



The length, l, is known. The p for perimeter and w for width are unknown.



c. Complete the sentence to describe the relationship between l, w, and P in words.



The perimeter equals twice the length plus twice the width.



If you know l and w and want to find P, multiply 2 times the length and add that to 2 times the width._



Solution Method 1



2. Solve the literal equation for the unknown variable. Be sure to show all the steps.



If the perimeter was given as 380, then 380 = 2(100) + 2w



380 = 200 + 2w



180 = 2w



w = 90



3. Complete the sentence to describe the relationship between l, w, and P in words.



If you know l and P and want to find w, take 2 times the length and subtract that from P. Divide that answer by 2 to find the width, w.



4. Show how you can use the new literal equation to find the width. Be sure to show all the steps.



(P - 2l)/2 = (380 - 200)/2 = 180/2 = 90



5. What is the width of the field?



If P was 380, then w = 90



Solution Method 2



6. Substitute the known information from the problem into the perimeter formula . Simplify where necessary. Then, solve the equation for the unknown variable. Be sure to show all the steps.



P = 2L + 2W



380 = 2(100) + 2W



380 = 200 + 2W



180 = 2W



W = 90



7. What is the width of the field?



If P = 380, then w = 90



Comparing Methods



8. Look back at the answers you found. The two methods should have produced the same answer. Which method did you prefer? Why? Explain your preference using at least three sentences.



The second method was shorter. It provided the answer quickly and easily. That makes it the easier, quicker solution.



I hope that helps!! :-)

Answer 2

first get all the units the same, in this case feet. 100 yards equals 300 feet. We are solving for W and now we know that 920ft = 2W + 2(300)ft or 920ft = 2W + 600ft or 920ft - 600ft = 2W or 320ft = 2W 320ft / 2 = W 160ft = W So the width of the field is 160ft. or 53 and 1/3 yards.

Answer 3

For a rectangle with perimeter = p, length = L, and width = w,

p = 2L + 2w