charlies swimming pool is rectangular. it has an area of 120ft2. charlie drew a scale drawing of the pool using the scale 3/2 centimeters= 2 feet. what was the area of the scale drawing?
To find the area of the scale drawing, we need to determine the dimensions of the pool in centimeters and then calculate the area using the scale.
Given:
Area of the rectangular pool = 120 ft^2
Scale: 3/2 cm = 2 ft
Step 1: Convert the area from square feet to square centimeters.
1 ft^2 = 929.03 cm^2 (approximately)
Therefore, the area of the pool in square centimeters is:
120 ft^2 * 929.03 cm^2/ft^2 = 111,683.6 cm^2 (approximately)
Step 2: Calculate the length and width of the pool in centimeters using the scale.
Since the length and width scale down by a factor of 3/2, we can write the following equations:
Length in cm = Length in ft * (3/2) cm/ft
Width in cm = Width in ft * (3/2) cm/ft
Let's represent the length in feet as L and the width in feet as W.
From the given information, we can also write:
Area of the pool = Length in ft * Width in ft
120 ft^2 = L * W
Using the scale, we can write:
111,683.6 cm^2 = L * (3/2) cm/ft * W * (3/2) cm/ft
Step 3: Solve the above equation for the product LW.
111,683.6 cm^2 = L * W * (9/4) cm^2/ft^2
To simplify, let's convert the cm^2/ft^2 to cm^2/cm^2 by multiplying by 929.03 cm^2/ft^2:
111,683.6 cm^2 = L * W * (9/4) cm^2/ft^2 * 929.03 cm^2/ft^2
Simplifying further:
111,683.6 cm^2 = L * W * (9/4) cm^2/cm^2 * 929.03 cm^2/ft^2
111,683.6 cm^2 = L * W * (9/4) cm^2
Dividing both sides by (9/4) cm^2:
111,683.6 cm^2 / (9/4) cm^2 = L * W
Finally, solve for the product LW:
Product LW = 111,683.6 cm^2 / (9/4) cm^2
Product LW = 49,603.2 cm^2
Hence, the area of the scale drawing is 49,603.2 cm^2.
To find the area of the scale drawing, we need to calculate the area of the actual swimming pool first.
Given that the area of the rectangular swimming pool is 120ft², we can represent the length of the pool as L ft and the width as W ft.
The formula for the area of a rectangle is A = L * W.
Substituting the given values, we have 120 = L * W.
Now, let's move on to finding the area of the scale drawing.
The scale given is 3/2 centimeters = 2 feet. This means that 3/2 centimeters on the scale drawing represent 2 feet in reality.
Since the area of the scale drawing should be proportional to the area of the actual swimming pool, we can set up a ratio using the scale.
Ratio of centimeters to feet: 3/2 cm = 2 ft
To find the area of the scale drawing, we need to consider the ratio in terms of area as well. Since area is a two-dimensional measurement, we need to square the scale ratio.
(3/2 cm)^2 = (2 ft)^2
(9/4) cm^2 = 4 ft^2
So, the area of the scale drawing is 9/4 cm².
Therefore, the area of the scale drawing is 9/4 cm².
the scale is 1.5cm/2ft = 0.0492
the area scales as .0492^2, so
a = (120ft^2)(30.48cm/ft)^2 * .0492^2 = 270 cm^2