Question

10. A rectangular yoga studio is 25.15 feet long and 13.62 feet wide.


A. Round the length and width to the nearest whole number. Then estimate the perimeter of the yoga studio. write an equation to model your work.


B. Round the length and width to the nearest tenth. Then estimate the perimeter of the yoga studio. write an equation to model your work.



c. Find the exact perimeter. which estimate is closer? Explain why you think that estimate is closer.



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Answer 1

Answer:

a.

$Length = 25$

$Width = 14$

$Perimeter = 78ft$

b.

$Length = 25.2$

$Width = 13.6$

$Perimeter = 77.6ft$

c.

$Perimeter = 77.54ft$

Estimate (b) is closer to the actual measurement.

Step-by-step explanation:

Given

$Length = 25.15$

$Width = 13.62$

Solving (a): Approximate measurements to whole numbers then estimate the perimeter.

When approximated to whole numbers (i.e. no decimal place), the new measurement is:

$Length = 25$

$Width = 14$

The perimeter is calculated as thus:

$Perimeter = 2(Length + Width)$

$Perimeter = 2(25 + 14)$

$Perimeter = 2*39$

$Perimeter = 78ft$

Solving (b): Approximate measurements to tenth then estimate the perimeter.

When approximated to tenth (i.e. to 1 decimal place), the new measurement is:

$Length = 25.2$

$Width = 13.6$

The perimeter is calculated as thus:

$Perimeter = 2(Length + Width)$

$Perimeter = 2(25.2 + 13.6)$

$Perimeter = 2*38.8$

$Perimeter = 77.6ft$

Solving (c): Exact Perimeter.

Given measurements are:

$Length = 25.15$

$Width = 13.62$

The perimeter is calculated as thus:

$Perimeter = 2(Length + Width)$

$Perimeter = 2(25.15 + 13.62)$

$Perimeter = 2*38.77$

$Perimeter = 77.54ft$

To determine which is nearest, we calculate the absolute difference between each estimate from the actual measurement.

For estimate a

$Difference = |77.54 - 78|$

$Difference = |-0.46|$

$Difference = 0.46ft$

For estimate b

$Difference = |77.54 - 77.6|$

$Difference = |-0.06|$

$Difference = 0.06ft$

The closest to the exact is the one with the smallest difference.

Hence, estimate (b) is closer to the actual measurement.