The dimensions of Sarah's apartment are 22 1/2 feet by 25 feet. In the drawing of the apartment below, 1 1/2 inches is equivalent to 15 feet. Complete the sentence below.
In the drawing, each side of the apartment is represented by ______ inches.
In the drawing of the apartment, 22 1/2 feet is equivalent to _____________ inches.
To complete the sentence, let's first convert the dimensions of Sarah's apartment to inches using the scale given.
We are given that 1 1/2 inches is equivalent to 15 feet. To convert feet to inches, we multiply by 12, so 1 1/2 inches is equivalent to 1.5 * 12 = 18 inches.
Now, let's convert the dimensions of the apartment to inches:
Length = 22 1/2 feet * 12 inches/foot = 270 inches
Width = 25 feet * 12 inches/foot = 300 inches
Now, let's compare these dimensions to the scale:
Length: 270 inches
Width: 300 inches
Since the scale ratio is 1 1/2 inches = 15 feet, we can calculate how many inches are equivalent to the apartment dimensions by setting up a ratio:
1 1/2 inches / 15 feet = x inches / (dimension in feet)
Using this ratio, we can find the equivalent inches:
For the length:
1 1/2 inches / 15 feet = x inches / 22 1/2 feet
Cross-multiplying, we get:
(1 1/2 inches) * (22 1/2 feet) = (15 feet) * x inches
Calculating this expression:
(1.5 inches) * (22.5 feet) = (15 feet) * x inches
33.75 inches = 15x inches
Dividing both sides by 15, we get:
x inches = 33.75 inches / 15
x inches = 2.25 inches
For the width:
1 1/2 inches / 15 feet = x inches / 25 feet
Cross-multiplying, we get:
(1 1/2 inches) * (25 feet) = (15 feet) * x inches
Calculating this expression:
(1.5 inches) * (25 feet) = (15 feet) * x inches
37.5 inches = 15x inches
Dividing both sides by 15, we get:
x inches = 37.5 inches / 15
x inches = 2.5 inches
So, the dimensions of Sarah's apartment in the drawing are 2.25 inches by 2.5 inches.