Question

A scientist who studies insects enlarges a photograph of an elm leaf beetle. Every 2 inches in the photograph represents 8 mm on the actual beetle. The length of the beetle in the photograph is 12 inches. The width of the beetle in the photograph is ____. What are the length and width of the actual beetle? Show your work.

Option 1: The width of the beetle in the photograph is 48 mm.
Option 2: The width of the beetle in the photograph is 6 inches.
Option 3: The length of the actual beetle is 30 mm.
Option 4: The width of the actual beetle is 96 mm.

Answer 1

The width of the beetle in the photograph is 48 mm. The length of the actual beetle is 48 mm. The correct option is 1.

Step-by-step explanation:

To find the width of the beetle in the photograph, we need to use the scale given. Every 2 inches in the photograph represents 8 mm on the actual beetle. Since the length of the beetle in the photograph is 12 inches, we can set up the proportion:

2 inches in the photograph / 8 mm on the actual beetle = 12 inches in the photograph / x mm on the actual beetle

Cross multiplying, we get 2x = 12 * 8.

Solving for x, the width of the beetle in the photograph is 48 mm.

To find the actual length and width of the beetle, we can use the same scale. Since 2 inches in the photograph represents 8 mm on the actual beetle, we can set up the proportion:

2 inches in the photograph / 8 mm on the actual beetle = 12 inches in the photograph / y mm on the actual beetle

Cross multiplying, we get 2y = 12 * 8. Solving for y, the length of the actual beetle is 48 mm.

Therefore, the correct options are: Option 1: The width of the beetle in the photograph is 48 mm and Option 3: The length of the actual beetle is 48 mm.