Question

A square patio has an area of 215 square feet. How long is each side of the patio to the nearest 0.05 ?

Answer 1

Hint: In the first part of the question, we have been asked to calculate the length of each side of the patio. Since, the patio is square, the length of all its sides is equal and can be calculated by finding the square root of the given area of the patio. Now, for the second part of the question, we will check the length of the patio and then round it off to the nearest 0.05 after decimal. This will give us the required answer.

Complete step-by-step solution:
Let us first of all assign some terms that we are going to use in our solution. Let the area of the square patio be denoted by ‘A’. Then, this is given to us as:
$\Rightarrow A=215f{{t}^{2}}$
Now, let the length of each side of the square patio be denoted by ‘l’, then we need to find the value of this length.
Since, its given that the patio is square in shape, therefore we can write its area in terms of its length as follows:
$\Rightarrow A={{l}^{2}}$
Putting the value of area of the patio in the above equation, we get:
$\begin{align}
  & \Rightarrow 215f{{t}^{2}}={{l}^{2}} \\
 & \Rightarrow l=\sqrt{215f{{t}^{2}}} \\
 & \therefore l=14.663ft \\
\end{align}$
Thus, the length of each side of the square patio comes out to be 14.663 feet.
In the second step of our solution, we need to round off this length to the nearest 0.05 after the decimal. This can be done as follows:
$\Rightarrow 14.663ft\approx 14.65ft$
Thus, our final result is 14.65 feet .
Hence, the length of each side of the patio to the nearest 0.05 comes out to be 14.65 feet .

Note: While calculating the square root of any number, we should be quick and correct at the same time. This will save us some time which can prove to be very helpful in an examination. Also, while rounding off, we should be careful and check if the rounded off value meets the criteria posed in the problem.