Translate the following statement into a mathematical equation:
2 answers:
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Answer:
total area = w^2 + 13w + 36 ft^2
Explanation:
The final pool and the sideways will be as shown in the attachment
1- We will get the area of the pool:
length of pool = w + 5
width of pool = w
area of pool = length * width
area of pool = w (w+5) square ft ...........> I
2- We will get the area of the sideways:
The side way is composed of the two blue rectangles and the two green ones
Therefore:
area of sideway = 2(area of blue rectangle) + 2(area of green rectangle)
a- getting the area of the blue rectangle:
length = w + 5 + 2 + 2 = w+9
width = 2
area of blue rectangle = length * width
area of blue rectangle = 2(w+9) square ft ..........> a
b- getting the area of the green rectangle:
length = w
width = 2
area of green rectangle = length * width
area of green rectangle = 2w square ft ..............> b
c- getting area of sideways:
as mentioned before:
area of sideways = 2(area of blue rectangle) + 2(area of green rectangle)
area of sideways = 2*equation a + 2*equation b
area of sideways = 2 (2(w+9)) + 2(2w)
area of sideways = 4(w+9) + 4w
area of sideways = 4w + 36 + 4w
area of sideways = 8w + 36 ...........> II
3- getting the total area:
total area = area of pool + area of sideways
total area = equation I + equation II
total area = w (w+5) + 8w + 36
total area = w^2 + 5w + 8w + 36
total area = w^2 + 13w + 36 ft^2
Hope this helps :)
total area = w^2 + 13w + 36 ft^2
Explanation:
The final pool and the sideways will be as shown in the attachment
1- We will get the area of the pool:
length of pool = w + 5
width of pool = w
area of pool = length * width
area of pool = w (w+5) square ft ...........> I
2- We will get the area of the sideways:
The side way is composed of the two blue rectangles and the two green ones
Therefore:
area of sideway = 2(area of blue rectangle) + 2(area of green rectangle)
a- getting the area of the blue rectangle:
length = w + 5 + 2 + 2 = w+9
width = 2
area of blue rectangle = length * width
area of blue rectangle = 2(w+9) square ft ..........> a
b- getting the area of the green rectangle:
length = w
width = 2
area of green rectangle = length * width
area of green rectangle = 2w square ft ..............> b
c- getting area of sideways:
as mentioned before:
area of sideways = 2(area of blue rectangle) + 2(area of green rectangle)
area of sideways = 2*equation a + 2*equation b
area of sideways = 2 (2(w+9)) + 2(2w)
area of sideways = 4(w+9) + 4w
area of sideways = 4w + 36 + 4w
area of sideways = 8w + 36 ...........> II
3- getting the total area:
total area = area of pool + area of sideways
total area = equation I + equation II
total area = w (w+5) + 8w + 36
total area = w^2 + 5w + 8w + 36
total area = w^2 + 13w + 36 ft^2
Hope this helps :)