Question

question 4 (25 points) you are wanting to put hard wood flooring in your living room. you used your stride length to estimate the dimensions of your living room to be 18 feet by 20 feet. a more accurate measurement of your living room using a standard measuring device results in the dimensions of your living room being 22 feet by 24 feet. 1 box of hardwood will cover 20 square feet. you want to make sure that you buy enough hard wood to cover your living room. explain the effects that an error in measurement has on your estimated measurements by comparing them to the more accurate measurements. by using the estimated measurements, you will not have enough hardwood flooring to cover your living room. you will need to buy 9 more boxes. by using the estimated measurements, you will not have enough hardwood flooring to cover your living room. you will need to buy 8 more boxes. by using the estimated measurements, you will have enough hardwood flooring to cover your living room. you will even have some left over in case you have to replace a piece of the flooring. there is not enough information to compare the estimated measurements to the more accurate measurements.

Explanation:

Step1: Calculate estimated area

The estimated dimensions are 18 feet by 20 feet. The area formula for a rectangle is $A = l\times w$. So the estimated area $A_{est}=18\times20 = 360$ square - feet.

Step2: Calculate accurate area

The accurate dimensions are 22 feet by 24 feet. Using the area formula for a rectangle, the accurate area $A_{acc}=22\times24=528$ square - feet.

Step3: Calculate number of boxes based on estimates

Since 1 box covers 20 square feet, the number of boxes based on estimates $n_{est}=\frac{360}{20}=18$ boxes.

Step4: Calculate number of boxes based on accurate measurements

The number of boxes based on accurate measurements $n_{acc}=\frac{528}{20}=26.4$. Since we can't buy a fraction of a box, we need 27 boxes.

Step5: Find the difference in number of boxes

The difference in the number of boxes $\Delta n=n_{acc}-n_{est}=27 - 18=9$ boxes.

Answer:

By using the estimated measurements, you will not have enough hardwood flooring to cover your living room. You will need to buy 9 more boxes.