On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30cm^2. What is the actual area of the room?

Answer: 30 m^2

Just need help understanding the concept and putting it all together. I can't grasp it very well from the book. Please & Thanks for your time

30m^2

1:100

One square = 30cm
100 squares = 3,000cm
100cm = 1m
Therefore the answer is 30m^2

Thanks Bob

No problem! I'll be happy to explain it to you.

In this case, we have a floor plan drawn at a scale of 1:100. This means that every measurement on the floor plan represents 1/100th of the actual measurement.

Let's say that the length of the room on the floor plan is x centimeters. Since the scale is 1:100, the actual length of the room would be 100 times x centimeters, or 100x centimeters.

Similarly, the width of the room on the floor plan is y centimeters, and the actual width of the room would be 100 times y centimeters, or 100y centimeters.

Now, we know that the area of a rectangle is calculated by multiplying its length by its width. So, the area of the room on the floor plan would be x * y square centimeters.

Using the scale of 1:100, the actual area of the room would be (100x) * (100y) square centimeters, which simplifies to 10,000xy square centimeters.

Given that the area of the room on the floor plan is 30 square centimeters, we can set up the equation x * y = 30. Rearranging the equation, we have xy = 30.

Now, to find the actual area of the room, we substitute the value of xy into the formula we derived earlier: 10,000xy. Since xy = 30, we can substitute 30 into the formula and get the actual area of the room as 10,000 * 30 = 300,000 square centimeters.

However, the question asks for the answer in square meters, not square centimeters. To convert the area from square centimeters to square meters, we divide by 10,000 (since there are 10,000 square centimeters in 1 square meter).

So, the actual area of the room is 300,000 / 10,000 = 30 square meters.

I hope this explanation helps you understand the concept better. Let me know if you have any further questions!

fghfguyg

if the scale is a:b (in this case 1:100), then the area is of scale a^2:b^2 (in this case, 1:100^2; or 1 to 10,000)

so if the scale area is 30cm^2, the real area is 30*10,000 cm^2
now the units: 100cm=1m
and in area (100cm)^2=1m^2 or
10,000 cm^2=1m^2
so a real area of 30x10,000cm^2= 1 m^2