he length of a wall in a floor plan is 6 1/2 inches.the actual wall is 78 feet long. find the scale of the floor plan
The height of a building is 3 3/8 inches on a scale drawing. Find the actual height of the building if the scale used is 1inch:4feet.
help please, this is really important to my grade.....
If it's very important to your grade, then it's very important that try to do it yourself.
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i think its 1"= 12 ft 0r 1: 144
To find the scale of the floor plan, we can set up a proportion using the length of the wall in the floor plan and the actual length of the wall.
Let's assume x represents the scale of the floor plan.
We know that 6 1/2 inches on the floor plan represents 78 feet in reality.
Setting up the proportion, we have:
6 1/2 inches / x = 78 feet / 1
To solve for x, we can cross-multiply:
(6 1/2 inches) * 1 = 78 feet * x
(13/2 inches) = 78 feet * x
Next, we can convert the measurements to the same units. Since 1 foot is equal to 12 inches, we have:
13/2 inches = 78 * x inches
Now, we can solve for x:
x = (13/2 inches) / (78 inches)
x = (13/2) / (78/12)
x = (13/2) * (12/78)
x = 156/156
x = 1
Therefore, the scale of the floor plan is 1 inch represents 1 foot.
Moving on to the second problem:
To find the actual height of the building, we can again set up a proportion using the height on the scale drawing and the scale.
Let's assume y represents the actual height of the building in feet.
We know that 3 3/8 inches on the scale drawing represents 1 inch to 4 feet in reality.
Setting up the proportion, we have:
3 3/8 inches / y = 1 inch / 4 feet
To solve for y, we can cross-multiply:
(3 3/8 inches) * 4 feet = 1 inch * y
(27/8 inches) = 1 inch * y
Now, we can convert the measurements to the same units. Since 1 foot is equal to 12 inches, we have:
(27/8 inches) = 1 * y feet
Now solve for y:
y = (27/8 inches) / 1
y = (27/8) / 1
y = 27/8
Therefore, the actual height of the building is 27/8 feet.
To find the scale of the floor plan, you need to determine the ratio between the length on the floor plan and the actual length.
In this case, the length on the floor plan is 6 1/2 inches, and the actual length is 78 feet.
To find the scale, you can set up a proportion:
Length on floor plan / Actual length = Scale
Substituting the given values:
6 1/2 / 78 = Scale
To simplify the fraction, convert the mixed number 6 1/2 to an improper fraction. Multiply 6 by the denominator (2) and add the numerator (1) to get 13. The fraction becomes 13/2.
(13/2) / 78 = Scale
To divide fractions, you need to flip the second fraction and multiply:
(13/2) * (1/78) = Scale
To simplify, cancel out common factors:
(13/1) * (1/78) = Scale
Multiply the numerators (13 * 1) and the denominators (1 * 78) to get:
13/78 = Scale
Simplifying the fraction, you get:
1/6 = Scale
Therefore, the scale of the floor plan is 1 inch to 6 feet.
Now, let's move on to the second problem.
In this case, the height on the scale drawing is 3 3/8 inches, and the scale used is 1 inch to 4 feet.
To find the actual height of the building, we need to set up a proportion using the scale:
Height on scale drawing / Actual height = Scale
Substituting the given values:
3 3/8 / Actual height = 1 inch / 4 feet
First, convert the mixed number 3 3/8 to an improper fraction. Multiply 3 by the denominator (8) and add the numerator (3) to get 27. The fraction becomes 27/8.
(27/8) / Actual height = 1/4
To solve for the actual height, we first need to isolate the variable by multiplying both sides of the equation by the reciprocal of (27/8). The reciprocal of (27/8) is (8/27).
(27/8) * (8/27) / Actual height = (1/4) * (8/27)
On the left side, (27/8) * (8/27) simplifies to 1.
1 / Actual height = (1/4) * (8/27)
To simplify the right side, multiply the numerators (1 * 8) and the denominators (4 * 27) to get:
1 / Actual height = 8/108
Simplifying the fraction, you get:
1 / Actual height = 1/13.5
To isolate the actual height, we can take the reciprocal of both sides:
Actual height = 1 / (1/13.5)
To divide by a fraction, multiply by its reciprocal:
Actual height = 1 * (13.5/1)
Actual height = 13.5 feet
Therefore, the actual height of the building is 13.5 feet.