Final answer:
Each inch on the neighbor's diagram represents 2.5 yards of the actual lawn. Multiplying the diagram's length in inches by this scale gives the actual length (12.5 yards), which, when multiplied by the actual width (20 yards), results in an area of 250 square yards.
Step-by-step explanation:
To calculate the area of the actual lawn that Emmanuel will have to mow, we need to understand the scale of the diagram and apply it to the actual measurements. The given width of the actual lawn is 20 yards, and the width on the diagram is 8 inches. This means each inch on the diagram represents 2.5 yards in reality (20 yards ÷ 8 inches = 2.5 yards). The length of the lawn on the diagram is 5 inches, which means the actual length of the lawn is 5 inches × 2.5 yards/inch = 12.5 yards.
Now we can calculate the area of the lawn by multiplying the actual length and width: Area = Length × Width = 12.5 yards × 20 yards = 250 square yards. Since 250 square yards is not one of the choices provided, we may need to check if there is an error in the question or the answer choices given. However, based on the information provided, none of the answer choices a) 100 square yards, b) 160 square yards, c) 200 square yards, or d) 400 square yards are correct.