the 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.

This is basically ratios and proportions, pleas help

each inch on the plan represents 12 actual feet, because 6.5 * 12 = 78 (78ft / 6.5in) = 12ft/in

3 3/8 * 4 = 13 1/2 ft

Oh, ratios and proportions? I guess it's time for some mathematical clowning around! Let's tackle these problems one at a time, shall we?

For the first problem, we have a length of 6 1/2 inches on the floor plan and the actual length is 78 feet. So we can set up the proportion:

6 1/2 inches / 78 feet = x / 1

Now, let's cross multiply and solve for x:

6 1/2 inches * 1 = 78 feet * x

And after some calculation...

(13/2) inches = 78 feet * x

Now, let me just use a little clown magic to convert inches to feet:

(13/2) * 1/12 = 78 feet * x

And of course, we have to solve for x:

(13/24) = 78 feet * x

Now, let's find that scale by dividing both sides by 78 feet:

(13/24) ÷ 78 feet = x

Drumroll, please...

x = (13/24) ÷ 78 feet

So, the scale of the floor plan is approximately (13/1872) feet:1. Aren't numbers funny?

Now, let's move onto the second problem:

We have a height of 3 3/8 inches on the scale drawing, and the scale used is 1 inch: 4 feet. To find the actual height of the building, we can set up the proportion:

3 3/8 inches / 1 = x feet / 4 feet

And let's use our clown arithmetic again:

(27/8) inches = x feet / 4 feet

Multiply both sides by 4 feet:

(27/8) inches * 4 feet = x feet

Guess what? It's time for a little clown magic again! Let's convert inches to feet:

(27/8) * 1/12 = x feet

And after a bit of calculation...

(27/96) = x feet

Did someone say clown math? Let's simplify that fraction:

(9/32) = x feet

So, the actual height of the building is approximately 9/32 feet. Clown math at its finest!

Now, wasn't that a hilarious way to approach ratios and proportions? I hope I brought a smile to your face while solving these problems. Remember, laughter is the best medicine for math troubles!

To find the scale of the floor plan, we can use the formula:

Scale = Actual Length / Length on Floor Plan

Given:
Length on floor plan = 6 1/2 inches
Actual Length = 78 feet

Let's convert both lengths to the same unit before calculating the scale. Converting feet to inches, we have:
Actual Length = 78 feet x 12 inches/foot = 936 inches

Now, we can calculate the scale:
Scale = Actual Length / Length on Floor Plan
Scale = 936 inches / 6 1/2 inches

To simplify the calculation, let's convert the mixed fraction (6 1/2) to an improper fraction:
6 1/2 inches = (6 x 2 + 1) / 2 = 13/2 inches

Now, substitute the values into the equation:
Scale = 936 inches / (13/2) inches

To divide by a fraction, we can multiply by its reciprocal:
Scale = 936 inches x (2/13) inches
Scale = 72 inches

Therefore, the scale of the floor plan is 72 inches.

Next, let's find the actual height of the building in the second scenario.

Given:
Height on scale drawing = 3 3/8 inches
Scale = 1 inch : 4 feet

To find the actual height, we can use the formula:
Actual Height = Height on Scale Drawing x Scale

First, convert the mixed fraction (3 3/8) to an improper fraction:
3 3/8 inches = (3 x 8 + 3) / 8 = 27/8 inches

Now, substitute the values into the equation:
Actual Height = 27/8 inches x 4 feet/inch

To multiply a fraction by a whole number, multiply the numerator by the whole number:
Actual Height = (27/8) inches x 4 feet/inch = (27 x 4) / 8 feet

Simplify the fraction:
Actual Height = 108/8 feet = 13.5 feet

Therefore, the actual height of the building is 13.5 feet.

To find the scale of a floor plan, you need to determine the ratio between the length on the floor plan and the actual length of the wall.

Let's use the given information to solve the first problem:

The length of the wall on the floor plan is 6 1/2 inches, and the actual length of the wall is 78 feet.

You want to find the scale, which is the ratio of the length on the floor plan to the actual length.

We can set up the proportion as follows:

Length on floor plan / Actual length = Scale

Substitute the given values:

6 1/2 inches / 78 feet = Scale

To solve this proportion, we need to convert the measurements to the same units. In this case, let's convert both measurements to inches:

6 1/2 inches = 6.5 inches (since 1/2 inch = 0.5 inches)
78 feet = 78 feet * 12 inches/foot = 936 inches

Now, the proportion becomes:

6.5 inches / 936 inches = Scale

Simplify the proportion:

0.0069 = Scale

So, the scale of the floor plan in this case is approximately 0.0069.

Now, let's move on to the second problem:

The height of the building on the scale drawing is 3 3/8 inches, and the scale used is 1 inch:4 feet.

You want to find the actual height of the building.

We can set up the proportion as follows:

Height on scale drawing / Actual height = Scale

Substitute the given values:

3 3/8 inches / Actual height = 1 inch / 4 feet

To solve this proportion, we need to convert the units. Let's convert the inches to feet:

3 3/8 inches = 3.375 inches (since 3/8 inch = 0.375 inches)

1 inch = 1 inch * 1 foot / 12 inches = 1/12 feet

Now, the proportion becomes:

3.375 inches / Actual height = 1/12 feet / 4 feet

Simplify the proportion:

3.375 inches / Actual height = 1/48

To solve for the actual height, we cross-multiply:

3.375 inches * 48 = Actual height

Actual height = 162 inches

However, since the question asks for the actual height in feet, we need to convert inches to feet:

Actual height = 162 inches * 1 foot / 12 inches = 13.5 feet

So, the actual height of the building is 13.5 feet.