Finding the Side Length of a Square Patio with Area 200 Square Feet
Apply the seven-step problem-solving strategy using the square area formula to find an unknown side length, producing a non-perfect-square result that must be rounded.
Problem: Mike and Lychelle want to make a square patio. They have enough concrete to pave an area of 200 square feet. Find the length of each side of the patio, rounded to the nearest tenth of a foot.
- Read: A square patio has square feet. Draw and label a square with sides .
- Identify: The length of a side of the square patio.
- Name: Let = the length of a side.
- Translate: Write the side-length formula and substitute the given area:
- Solve: Evaluate: .
- Check: , which is close to 200. The small discrepancy is due to rounding the square root. A patio with side 14.1 feet is a reasonable size.
- Answer: Each side of the patio should be 14.1 feet.
Because 200 is not a perfect square, the exact side length is an irrational number that cannot be expressed as a terminating decimal. Rounding to the nearest tenth and then checking by squaring confirms the answer is close enough for a real-world application.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Finding the Hypotenuse of a 3-4-5 Right Triangle
Finding the Perimeter of a 32-by-20-Meter Rectangle
Finding the Width of a Rectangular Room Given Its Area
Finding the Length of a Rectangle Given Its Perimeter and Width
Finding Rectangle Dimensions When Width Is Defined in Terms of Length
Finding Swimming Pool Dimensions Given Its Perimeter
Finding the Side Length of a Square Patio with Area 200 Square Feet
A facilities coordinator is planning to install new safety fencing around a rectangular equipment yard. To ensure the project is calculated accurately using the standard geometry problem-solving strategy, arrange the following steps in the correct order from start to finish.
A construction site supervisor is training a new intern on how to approach layout calculations for a rectangular foundation. According to the seven-step problem-solving strategy for geometry applications, what specific visual task should be completed during the 'Read' phase to ensure all measurements are correctly organized?
A facilities coordinator is planning the layout of a new rectangular storage extension for a logistics center. To ensure the project follows the standard seven-step problem-solving strategy for geometry applications, match each step name with the specific action required to complete it.
Visual Rationale in Geometry Strategy
An HVAC technician is using the seven-step problem-solving strategy to solve a geometry-based layout problem. According to the first step of this strategy, after reading the problem, the technician must ________ the figure and label it with the given information to organize the measurements visually.
Finalizing a Flooring Project
Steps of the Geometry Problem-Solving Strategy
According to the seven-step problem-solving strategy for geometry applications, sketching a diagram and labeling it with measurements should be performed during the first step of the process.
A facilities manager is using the seven-step problem-solving strategy to calculate the area of a new rectangular parking lot. According to this strategy, which specific action should be performed during the 'Translate' step?
A warehouse manager is finalizing the calculations for the area of a new loading dock. After checking the answer and confirming it is correct (Step 6), what is the final action required in Step 7 of the geometry problem-solving strategy?
Finding Right Triangle Angles When One Is Expressed Relative to Another
Finding a Leg of a 5-12-13 Right Triangle
Finding the Height of a Triangle Given Its Area and Base
Finding the Base of a Triangle Given Its Area and Height
Learn After
A contractor is building a square patio with a total area of 200 square feet. Which formula is used to find the length of one side (s)?
A project manager is calculating the dimensions for a square concrete pad with an area of 200 square feet. Arrange the following steps of the problem-solving strategy in the correct order to determine the side length.
A project estimator is calculating the dimensions for a square storage unit that has an area of 200 square feet. Following the formula , the side length, rounded to the nearest tenth of a foot, is ____ feet.
A project estimator is finalizing the plans for a square concrete foundation that covers an area of 200 square feet. Match each project component with its correct mathematical formula or numerical value as used in the standard estimation process.
Analysis of Rounding in Area Estimation
A project estimator is calculating the side length of a square storage unit that covers an area of 200 square feet. Because 200 is not a perfect square, the exact length of each side is an irrational number.
Quality Assurance for Concrete Foundations
Procedural Documentation for Square Area Dimensions
A project estimator is verifying the dimensions of a square patio with an area of 200 square feet. After calculating the side length as 14.1 feet, the estimator performs a check and finds that 14.1 squared is 198.81. According to the standard problem-solving strategy, what is the primary reason for this discrepancy?
A project estimator is using a seven-step strategy to determine the side length of a 200-square-foot square patio. Which step of the strategy specifically involves writing the formula and substituting the known area value into that equation?