a large square room has an area of 144 m2 . a) find the length of a side of the room. b) how much baseboard is needed to go around the room? c) each piece of baseboard is 2.5 m long. how many pieces of baseboard are needed?
Answers
Part (a)
area = (side)^2
side = sqrt(area)
side = sqrt(144)
side = 12 meters
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Part (b)
perimeter = 4*(side)
perimeter = 4*12
perimeter = 48
Therefore, you'll need 48 meters of baseboard.
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Part (c)
n = number of pieces
2.5n = total length of all n baseboards
2.5n = total perimeter
2.5n = 48
n = 48/2.5
n = 19.2
Round this up to the nearest whole number. Do not round to n = 19 as that value is too small. Note how 2.5n = 2.5*19 = 47.5 meters, which is 0.5 meters short of the goal of 48 meters.
But if n = 20 then 2.5n = 2.5*20 = 50 meters. We'll have 2 extra meters of baseboard.
Therefore, you need 20 pieces of baseboard.
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Answers:
(a) side length = 12 meters
(b) 48 meters of baseboard
(c) 20 pieces
Final answer:
The length of a side of a room with an area of 144m^2 is 12m. The total amount of baseboard needed is the perimeter, which is 48m. If each piece of baseboard is 2.5m, then you would need 20 pieces to cover the room.
Explanation:
The area of a square is calculated by squaring the length of one of its sides. Therefore, if the area is 144m2, the length of one side can be found by taking the square root of the area, which is 12m.
Baseboard is usually required to be placed around the entire room, so you'd need to find the perimeter of the square. The perimeter of a square is four times the length of one side, therefore, 12m x 4 = 48m.
As for the number of baseboard pieces, each piece is 2.5m long. So the total number of pieces needed would be the total length of baseboard (48m) divided by the length of each piece (2.5m). This equals 19.2, but since you can't use 0.2 of a piece, you'd need to round up, resulting in 20 pieces being needed.
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