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Algebra 1

7.1.2 The Relationship between Length and Area

Algebra 17.1.2 The Relationship between Length and Area

7.1.2 The Relationship between Length and Area

7.1.2 • The Relationship between Length and Area

Activity

Noah has 50 meters of fencing to completely enclose a rectangular garden in the backyard.

1.

Draw some possible diagrams of Noah’s garden. Label the length and width of each rectangle.

2.

Find the length and width of a rectangle that would produce the largest possible area. Explain why you think that pair of length and width gives the largest possible area.

Self Check

Sonya has 70 meters of fencing to surround a rectangular garden. What is the largest possible area that can be enclosed, in square meters?
  1. 1225
  2. 306.25
  3. 35
  4. 17.5

Additional Resources

Largest Possible Area

Tyrel is enclosing a grassy area for his goats. He has 80 feet of fencing and wants to make a rectangular enclosed area. What are the dimensions of the enclosure with the largest possible area?

First, make a table with possible length and width dimensions and their areas. Remember, each 2l+2w=802l+2w=80 and A=lwA=lw.

Length (meters) Width (meters) Area (square meters)
5 35 175
10 30 300
15 25 375
20 20 400
25 15 375
30 10 300
35 5 175

Notice that the closer the rectangle is to a square, the larger the area.

The largest area occurs when the length and width are both 20 feet for an area of 400 square feet.

Try it

Largest Possible Area

Elena has 100 feet of fencing to make a rectangular pen for her cow. What is the largest possible area she can make with this amount of fencing?

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