Question

Farmer Jack wants to fence his two fields. Answer the following questions:

a) About how much fencing is needed in total?

b) The total amount of fencing for both the corn and the carrot field is the same as that needed for a wheat field. If the wheat field is also in the shape of a square, what is its side length?

c) "My field is in the shape of a square too. The side length of my field is 2 times that of farmer Jack's wheat field. Is the area of my field to times that of farmer Jack's wheat field?"

Answer 1

Explanation:

a) To fence off each field, we need to know the length of each side. For a square field, the area is equal to the length of one side squared. So for the carrot field, we have:

area = side^2

10 km^2 = side^2

side ≈ 3.16 km

Similarly, for the corn field, we have:

5 km^2 = side^2

side ≈ 2.24 km

To find the total amount of fence needed, we need to add up the lengths of all four sides of both fields:

total fence = 4 × (3.16 km + 2.24 km) ≈ 20.8 km

So approximately 20.8 km of fence is needed in total.

b) The total amount of fencing needed for the wheat field is the same as the total amount of fencing needed for the carrot and corn fields combined. We already know that the total amount of fencing needed for the carrot and corn fields is approximately 20.8 km. For a square wheat field, all four sides are the same length, so we can let "x" be the length of one side. Then we have:

4x = 20.8 km

x ≈ 5.2 km

So the length of one side of the wheat field is approximately 5.2 km.

c) If the length of one side of the wheat field is x, then its area is x^2. The area of the other square field is 2x^2 (since its side length is 2 times that of the wheat field). So the product of the two areas is:

x^2 × 2x^2 = 2x^4

So the area of the other field is indeed multiplied by that of Farmer Jack's wheat field.