will a 150 foot rope be enough to cover an area of 1450 square feet?

Question

you plan to use a square section of a park for a small outdoor concert. The section should have an area of 1450 square feet. You have 150 feet of rope to use, to surround the section. Do you have enough rope. Explain your reasoning.

Answer 1

SQUARE:

If it had to be a square, your perimeter would be 150. Since there are 4 sides to square, that's 37.5 feet for each side. Area of a square is s² = 37.5² = 1406.25 sq. feet.

This is smaller than your desired 1450 sq. feet, so you couldn't do it.

- - - - - - - - -
CIRCLE: *this isn't the question, but consider it "extra credit"

If you could make it a circle, then you have:
C = pi x d
d = 150 / pi
r = d/2 = 75 / pi = 23.8 ft. radius.

Then the area would be:
A = pi x r²
A = pi x 75/pi x 75/pi
A = 75² / pi
A = 1790.5 sq. feet

So if you make the area a circle, with a radius of 23.8 feet, you can easily enclose more than 1450 sq. feet.
- - - - - - -
Anyway, back to the question... you *cannot* enclose a square area of 1450 sq. feet using 150 feet of rope.

Answer 2

If you're using a square section that means all sides are the same length - say 'L'. Without doing the problem for you, you need to compare the area of the square with the perimeter.

Area for a square would be one side times another - or L^2 = 1450

Perimeter would be all 4 sides added together - L+L+L+L or 4L.

You need figure those out to know if the 4L will be less than 150.

Answer 3

Area you talking about a square/rectangle/circle area

P = 2(x + y)
A = xy

150 = 2(x + y)
x + y = 75

x = -y + 75

1450 = (-y + 75)y
1450 = -y^2 + 75y
-y^2 + 75y - 1450 = 0
y^2 - 75y + 1450 = 0

You will get no with this one

----------------------------------------

P = 4x
A = x^2

1450 = x^2
x = sqrt(1450)

P = 4sqrt(1450)
P = about 152 ft

Then No

---------------------------------

A = pi * r^2
1450 = pi * r^2
1450/pi = r^2
r = sqrt(1450/pi)

C = 2pi * r
C = 2pi * sqrt(1450/pi)
C = about 1345

Then Yes

So it really all depends on what kind of area you are wanting to cover.

Answer 4

no it will be 1406