Finding Side Length of Square Window from Area Square Root Calculation

Published on March 13, 2026

Pre-Algebra

Calculate the side length of a square window given its area (18.4 ft^2) by taking the square root and comparing the result to the nearest provided option.

Question

Answer

Here is the step-by-step solution to the problem.

1. Understand the problem and identify the given information:

The window is square.
The area covered by the contact paper is .
Since the paper completely covered the square window without overlap, the area of the contact paper equals the area of the square window.
We need to find the side length of the window, , in feet, and determine which option is closest.

2. Recall the formula for the area of a square:
The area (

) of a square with side length (

) is given by:

3. Set up the equation:
We are given

.

4. Solve for the side length ():
To find

, we take the square root of the area:

5. Calculate the approximate value of :
We need to find the square root of 18.4. We can estimate this by looking at perfect squares near 18.4:

Since

, the side length

must be between 4 feet and 5 feet.

Let’s calculate the square roots of the options provided or test the options:

Option A: If , . (Difference from 18.4 is )
Option B: If , . (Difference from 18.4 is )
Option C: If , . (Difference from 18.4 is )
Option D: If , . (Difference from 18.4 is )

To find the closest measurement, we calculate the actual value of

:

6. Compare the result to the options:
The actual side length is approximately

.

Difference between and (Option A):
Difference between and (Option B):
Difference between and (Option C):
Difference between and (Option D):

The smallest difference is

, which corresponds to the side length of

.

Answer:
The measurement closest to the side length of the window is

. This corresponds to option B.

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features