Your parents decide they would like to install a rectangular swimming pool in the backyard. There is a 15-foot by 20-foot rectan
gular area available. Your parents request a 3-foot edge around each side of the pool. Draw a diagram of this situation in a coordinate plane. What is the perimeter and area of the largest swimming pool that will fit?
1 answer:
Answer:
- perimeter: 46 ft
- area: 126 ft²
Step-by-step explanation:
Since the 3 ft edge is on both sides of the pool, each dimension of the pool is 6 ft shorter than the corresponding dimension of the space. The pool will be 15 ft -6 ft = 9 ft in one direction and 20 ft -6 ft = 14 ft in the other direction.
The perimeter of the pool is the sum of its side lengths:
P = 9 ft + 14 ft + 9 ft + 14 ft = 2(9 ft +14 ft) = 2(23 ft)
P = 46 ft
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The area of the pool is the product of its length and width:
A = (14 ft)(9 ft) = 126 ft²
The perimeter and area are 46 ft and 126 ft², respectively.
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Given data is 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22
Arranging it in increasing order:
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Number of data items, n=15.
Finding Median, First Quartile, and Third Quartile
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Now finding First Quartile from set: 22 25 34 35 41 41 46
Q₁ = middle term i.e. 35
Now finding Third Quartile from set: 46 47 49 54 54 59 60
Q₃ = middle term i.e. 54
So we have Q₁ = 35, M = 46, and Q₃ = 54. Lower bound is 22 and Upper bound is 60.
While drawing the given data on number line and marking First quartile, Median, Third quartile on number line. We can clearly observe that option A matches with given data points.
Hence, option A i.e. Box-plot A is the correct choice.