An architect created a scale drawing of a statue using a scale in which 0.50 inch in the scale drawing represents 3 feet in the real world. The height of the actual statue is 114 feet.
What is the length in inches of the statue in the scale drawing?
38 inches
19 inches
50 inches
76 inches
To find the length in inches of the statue in the scale drawing, we first need to figure out the scale ratio.
The scale tells us that 0.50 inch in the scale drawing represents 3 feet in the real world. We can write this as a ratio:
0.50 inch / 3 feet
To find the scale ratio, we can simplify this ratio by dividing both the numerator and denominator by the greatest common divisor (GCD) of 0.50 and 3, which is 0.50 (since 3 / 0.50 = 6).
0.50 inch / 3 feet simplifies to:
0.5 / 0.50 inch / 6 feet
Dividing 0.50 by 0.50 gives us 1, so the simplified scale ratio is:
1 inch / 6 feet
Now we can use this ratio to find the length in inches of the statue in the scale drawing.
The height of the actual statue is 114 feet. To find this height in inches according to the scale, we can set up a proportion:
1 inch / 6 feet = x inches / 114 feet
To solve for x, we can cross-multiply and divide:
6 feet * x inches = 1 inch * 114 feet
6x = 114
Dividing both sides of the equation by 6:
x = 114 / 6
x = 19
Therefore, the length in inches of the statue in the scale drawing is 19 inches. The correct answer is B) 19 inches.