Question

A scientist who studies insects enlarges a photograph of an elm leaf beetle. Every 2 inches in the photograph represents 8mm on the actual beetle. The length of the beetle in the photograph is 1.5 inches. The width of the beetle in the photograph is 0.75 inches. What is the area of the photograph of the beetle in numbers only, rounded to the hundredths place?

Answer 1

The area of the photograph of the beetle is 18 mm².

Step-by-step explanation:

To find the area of the beetle in the photograph, we need to convert the measurements from inches to millimeters. Since every 2 inches in the photograph represents 8mm on the actual beetle, we can set up a proportion to find the actual length and width of the beetle. Using the given length of 1.5 inches, we have:

1.5 inches = x millimeters

2 inches = 8 millimeters

Cross-multiplying, we have 2x = 1.5 * 8

Simplifying, we find that x = 6 millimeters.

Similarly, using the given width of 0.75 inches, we have:

0.75 inches = y millimeters

2 inches = 8 millimeters

Again, cross-multiplying, we have 2y = 0.75 * 8

Simplifying, we find that y = 3 millimeters.

Now that we have the actual length and width in millimeters, we can find the area by multiplying the length and width. The area is given by:

Area = length * width

Area = 6mm * 3mm

Area = 18 mm^2