Rihanna planned a rectangular courtyard for a park and made a scale drawing using inches as the unit of measurement. She originally planned for the length of the actual courtyard to be 54 feet, but she decided to change it to 72 feet. If the length of the courtyard is 18 inches in her scale drawing, which statement about the change of scale is true?
these are the options:
One inch represented 1 foot in the first scale, but now 1 inch represents 4 feet in the second scale.
One inch represented 4 feet in the first scale, but now 1 inch represents 3 feet in the second scale.
One inch represented 54 feet in the first scale, but now 1 inch represents 72 feet in the second scale.
One inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale.
To determine which statement about the change of scale is true, we need to compare the original length in the scale drawing to the revised length.
Given that the original length of the actual courtyard is 54 feet and the length in the scale drawing is 18 inches, we can set up a ratio to represent the scale:
Original length in scale drawing / Actual length = scale factor
18 inches / 54 feet = scale factor
To compare the revised length, we can use the same scale factor:
Revised length in scale drawing / Actual length = scale factor
Let's substitute the revised length (72 feet) into the equation:
Revised length in scale drawing / 72 feet = 18 inches / 54 feet
To solve this equation, we can cross-multiply:
(Revised length in scale drawing) * 54 feet = 18 inches * 72 feet
Dividing both sides of the equation by 54 feet gives:
Revised length in scale drawing = (18 inches * 72 feet) / 54 feet
Simplifying this expression:
Revised length in scale drawing = 24 inches
Now, we can compare the original length in the scale drawing (18 inches) to the revised length in the scale drawing (24 inches):
18 inches < 24 inches
Therefore, the true statement about the change of scale is that the revised length in the scale drawing is greater than the original length.