Question

Zoeys's pool is shaped like a square with an area of 150 square feet. What is the approximate side length of her pool?

Hint: first determine which two perfect squares it is between, then determine which it is closest to.

*Estimate to the tenths place, don't forget units!*

Answer 1

The side length of the pool is approximately 12.2 feet.

Explanation:

Estimation

The area of a square of side length a is given by:

`A = a^2`

If the area is known, then the side length is:

`A = a^2`

We are given Zoeys' pool is a square with an area of 150 square feet.

Then:

`a=√(150)`

Since 150 does not have an exact square root value, we must estimate by successive approximations.

First, find the two integers perfect squares between which it's located.

Note
`12^2=144`,
`13^2=169`

The square root is between 12 and 13.

Since 150 is closer to 144 than to 169, the square root is closer to 12 than to 13.

Now we increase from 12 to 12.1:

`12.1^2=146.41`

`12.2^2=148.84`

`12.3^2=151.29`

Note that 150-148.84 = 1.16 and 151.29-150 = 1.29

The answer is closer to 12.2 than to 12.3, thus:

The side length of the pool is approximately 12.2 feet.