A circular pol is to be built in a back yard. The yard forms a 40ft by 60ft rectangle. The pool will have a diameter of 29ft.

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To find out if the circular pool can fit within the rectangular backyard, we need to compare the dimensions of the pool and the yard.

Given:
Rectangle yard dimensions: 40ft by 60ft
Circular pool diameter: 29ft

First, let's consider the area of the pool and the area of the yard.

1. Calculate the area of the pool:
To find the area of a circle, we use the formula: A = π * r^2, where A is the area and r is the radius.
Since the diameter is given, we can find the radius by dividing the diameter by 2: r = 29ft / 2 = 14.5ft.
Now, calculate the area: A = π * (14.5ft)^2.

2. Calculate the area of the yard:
The area of a rectangle is given by multiplying the length by the width: A = length * width.
For the given yard dimensions, the area is: A = 40ft * 60ft.

Now, let's compare the areas to see if the pool can fit within the yard.

If the area of the pool is less than or equal to the area of the yard, the circular pool will fit.

If the area of the pool is greater than the area of the yard, the pool will not fit.

Calculate the areas:

Area of the pool:
A = π * (14.5ft)^2
A ≈ π * 210.25ft^2

Area of the yard:
A = 40ft * 60ft
A = 2400ft^2

Comparing the areas:
π * 210.25ft^2 ≈ 659.78ft^2
2400ft^2

The area of the circular pool is approximately 659.78ft^2, while the area of the rectangular yard is 2400ft^2.

Since the area of the pool is less than the area of the yard, the circular pool can fit within the rectangular backyard.