Calculate the length and the width of the rectangle using the Ruler Postulate.
B
b
Let each zucchini get an area in the shape of a square.
C
c
Do you already know the size of the lettuce field?
A
a
A=72 square feet.
B8
b
C7 zucchini plants and 36 heads of lettuce.
c
Practice makes perfect
a
Let's begin by creating a diagram showing the garden.
The garden is a rectangle and we find its area using the formula
A=l w
where l is the garden's length and w its width. Let's calculate l which is the same as the distance between the points T and Q. The points have the same x-coordinate. The length is therefore vertical and we can calculate the distance using the Ruler Postulate.
The garden's length is 12 feet. Let's calculate its width. We find the garden's width by calculating the length of the side TS. Since the length is vertical the width is, as a consequence, horizontal. We can therefore calculate the width using the Ruler Postulate.
The garden's width is 6 feet. We can now calculate the garden's area and it is
A=l w=12* 6=72 square feet.
b
Since one zucchini plant needs 9 square feet around it we can divide the garden into squares each with the area 9 square feet. In the middle of each of these squares we can then grow one zucchini plant. Let's calculate the side of a square with the area 9 square feet.
The squares will have a side which is 3 feet. Let's fit in as many such squares as possible in the garden.
When we count we find that we managed to fit in 8 squares each with the area 9 square feet. Therefore we can grow a total of
9 zucchini plants.
c
We have now decided to also grow some lettuce in our garden. Let's mark the square we intend to set aside for this.
That leaves us 7 squares in which we can grow one zucchini each. That is, we can grow a total of
7 zucchini plants.
The area we set aside to grow lettuce coincides precisely with one of the squares in which we previously grew zucchini. We, therefore, know that its area is 9 square feet. With four heads per square foot we can grow a total of
4* 9=36 lettuce heads.
