A rectangular room has an area of 120ft squared. Marge drew a scale drawing of the pool using the scale 1.5cm=2ft. What was the area of the scale drawing?
a) 213.3cm2
b) 67.5cm2
c)53.3cm2
d)1.5cm2
I don't think any of the choices match the answer (90cm2)?
After the scaling, the new shape is similar to the old shape
areas of similar shapes are proportional to the square of their sides
120 ft^2/2^2 = A/1.5^2
120/4 = A/2.25
A = 120(2.25)/4 = 67.5
OR
suppose the actual room was 10 ft by 12 ft ---> area = 120 ft^2
in our scale the room would be 7.5 cm by 9 cm
area of scaled room = 7.5(9) or 67.5 cm^2
To find the area of the scale drawing, we need to understand the relationship between the actual dimensions and the scaled dimensions given the scale of 1.5cm = 2ft.
First, let's find the dimensions of the rectangular room. We know that its area is 120ft^2, so we can find the length and width of the room by factoring the area into two numbers that multiply to give 120.
One possible combination is 12ft by 10ft since 12 * 10 = 120. However, there can be different combinations such as 6ft by 20ft or 4ft by 30ft, and so on. So, we need to consider all possible combinations.
Now that we have the dimensions of the room, we can find the dimensions of the scale drawing by applying the scale of 1.5cm = 2ft. Since the scale says 1.5cm represents 2ft, we can create a proportion to find the corresponding measurement in centimeters.
1.5cm / 2ft = x cm / y ft
To find the length and width of the scale drawing, we use the formula:
Length of scale drawing = Length of room in ft * (1.5cm / 2ft)
Width of scale drawing = Width of room in ft * (1.5cm / 2ft)
Now, let's solve for the length and width of the scale drawing.
Length of scale drawing = 12ft * (1.5cm / 2ft) = 9cm
Width of scale drawing = 10ft * (1.5cm / 2ft) = 7.5cm
To find the area of the scale drawing, we multiply the length and width:
Area of scale drawing = Length of scale drawing * Width of scale drawing
= 9cm * 7.5cm
= 67.5cm^2
Based on the calculations, it appears that none of the given answer choices match the correct area of the scale drawing (90cm^2). Perhaps there was an error in the question or answer choices provided.