Area

[Guest]

The number of feet around a square field is equivalent to the number of acres in the field. Determine area of the field.

My attempt:

Let X = Length of side in feet.

X * X = X^2 = Area

4X = Perimeter

4X = X^2 / 43560

174240X = X^2 (clearing)

X = 174240

X^2 / 43560 = 696960 acres

Where did I miscalculate ?

[Guest]

Please respond. Thanks again.

[Guest]

Your solution appears to be correct.
696960 acres = 30359577600 sq ft = (174240 ft)^2
Therefore the perimeter is 4 x 174240 = 696960 ft

There is also one other solution namely X=0 (Area = Perimeter = 0).
(When you were trying to solve the quadratic equation you divided by X, which is fine provided X is not 0).

Hope this helped,

R. Baber.

[Guest]

That helped. Thanks.

The original problem had used the number of rods around a square field. I wanted to use feet. That is the reason I was not sure about the calculations even though I knew the square feet in an acre.

One question:

How would the X = 0 be used ?

[Guest]

X = 0 feet
Area = X^2 = 0 sq ft = 0 acres
Perimeter = 4X = 0 feet
Perimeter in feet = Area in acres
So this is also a valid solution.

Hope this helped,

R. Baber.

[Guest]

Thanks - that helped.

[leesajohnson]

According to me, it is correct and there is no mistake.

[Guest]

OK..... Lets start at the very beginning.....a very good place to start.....

Lets consider 1 acre...... a square acre...there are 43560 square feet in 1 acre
So 1 Square acre is a square of sides 208.71 feet.
Let "A^2" be the area of the square field in acres
Then the length of the side of the square field is "A" feet
By "ratio and proportion" the square field is "A^2" times the area of our "1 square acre"
And the length of the side of the square field is "A" times the length of the side of our "1 square acre"
So the number of feet around the square field is 4 x 208.71 x A = 834.84A feet.
And we are told that this is the same as the number of acres in the square field.... A^2

So..... 834.84A = A^2

gives.... 834.84 = A

So acres in the "square field" is A^2 = 834.84 x 834.84 = 696957.82 acres
and the Length of the 4 sides around the "square field" = 834.84A = 834.84 x 834.84 = 696957.82 feet

[Guest]

Thank you again.