Shane and Karen want to measure the length of a soccer field. Should they use centimeters or meters to measure it? Explain.
2 answers:
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Answer:
Step-by-step explanation:
(a)
Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.
Let assume the length of the rectangle is 50;
Then, the breath can be calculated as follows:
= 50 × 5 = 250 ( since the breath is divided into 5 parallel sides)
The fencing is said to be 950 ft
So, 950 - 250 = 700
Then divided by 2, we get:
= 700/2
= 350
So for the first diagram; the length = 50 and the breath = 350
The area = 50 × 350 = 17500 ft²
Now, let's go up a little bit.
If the length increase to 100;
Then 100 × 5 = 500
⇒ 950 - 500 = 450
⇒ 450/2 = 225
The area = 225 × 100 = 22500 ft²
Suppose the length increases to 150
Then 150 × 5 = 750
⇒ 950 - 750 = 200
⇒ 200/2 = 100
The area = 150 × 100 = 15000 ft²
The diagrams for each of the outline above can be seen in the image attached below.
(b) The diagram illustrating the general solution can be seen in the second image provided below.
(c) The expression for the total area A in terms of both x and y is:
Area A = x×y
(d) Recall that:
The fencing is said to be 950 ft.
And the length is divided inside into 5 parallel sides;
Then:
5x + 2y = 950 (from the illustration in the second image below)
2y = 950 - 5x
(e)
From (c); replace the value of y in (d) into (c)
Then:
Area A = x×y
Open brackets
(f)
By differentiating what we have in (e)
x = 475/5
x = 95
From (d):
∴
Area A = x × y
Area A = 95 × 237.5
Area A = 22562.5 ft²
