Answer:
Length= 90 ft;
Width= 46 ft.
Step-by-step explanation:
This is a case of a system of linear equations. Solution:
Step 1. Name the variables.
Let the length be L.
Let the width be W.
Step 2. Now, state in equations the 2 requirements that have to be met:
First requirement: "The perimeter of a playing field for a certain sport is 272 ft". Knowing that the playing field has the shape of a rectangle, it's perimeter is given by the following equation:
2L+2W=272 ft.
Second requirement: "...the length is 44 ft longer than the width", with that we can state the following:
L=W+44
Step 3. Set up the linear equation system.
1) L=W+44
2) 2L+2W=272
Step 4. Take equation 1 and extract the value of L.
L=W+44
Step 5. Take the value of L and substitute it into equation 2.
2(W+44)+2W=272
Step 6. Solve for W.
2(W+44)+2W=272
2W+88+2W=272
4W+88=272
4W=272-88
4W=184
W=184/4
W=46
Step 7. Insert the value of W into equation 1 and find the value of L.
L=46+44
L= 90
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L= 90;
W= 46.
