Question

1. Charlene wants to center a rectangular pool in her backyard so that the edges of the pool are an equal distance from the edges of the yard on all sides. The yard currently measures 60 m by 50 m. She wants to use ½ of the area of the yard for the pool. Create an equation for the pool’s dimensions and solve for the distance the pool is from the edge of the yard. Round your final answer to the nearest tenth of a meter.

Answer 1

First, we have to calculate the length of the sides of the pool, we are told that the scale factor of the backyard to the pool size equals 1/2, then we can find the length of the sides of the pool by multiplying the lengths of the sides of the backyard by 1/2, like this:

length of the pool = length of the yard * 1/2

width of the pool = width of the yard * 1/2

By replacing the 60 m for the length of the yard and 50 m for the width, we get:

length of the pool = 60 * 1/2 = 30

width of the pool = 50 * 1/2 = 25

Let's call x1 to the distance from the base of the pool to the bottom side of the yard and x2 to the distance from the top side of the pool to the top side of the yard, then we can formulate the following equation:

width of the yard = width of the pool + x1 + x2

Since we want the edges to be at an equal distance, x1 and x2 are the same, then we can rewrite them as x:

width of the yard = width of the pool + x + x

width of the yard = width of the pool + 2x

Replacing the known values:

60 = 30 + 2x

From this equation, we can solve for x to get:

60 - 30 = 30 - 30 + 2x

30 = 2x

30/2 = 2x/2

15 = x

x = 15

Now, let's call y1 to the distance from the right side of the corresponding side of the yard and y2 to the distance from the left side of the pool to the left side of the yard, with this, we can formulate the following equation:

length of the yard = length of the pool + y1 + y2

Since we want the edges to be at an equal distance, y1 and y2 are the same, then we can rewrite them as y:

length of the yard = length of the pool + y + y

length of the yard = length of the pool + 2y

Replacing the known values:

50 = 25 + 2y

50 - 25 = 25 - 25 + 2y

25 = 2y

25/2 = 2y/2

12.5 = y

y = 12.5

Now, we know that the pool must be at a distance of 15 m from the horizontal sides of the pool to the horizontal sides of the yard and that it must be at a distance of 12.5 m from the vertical sides of the pool to the vertical sides of the yards.

Here is a figure that depicts the results: