Question

two students are discussing whose garden has the most area to plant flowers. the first student claims that all they have to do is walk around the two gardens to get the perimeter and the one with the greatest perimeter has the greatest area. how would you help these students? which is a correct response? a. the students are correct in comparing the perimeters of each garden, because the area of a garden does not depend on the perimeter of the garden b. the students need to compare the areas of each garden, because the area of a garden does depend on the perimeter of the garden c. the students are correct in comparing the perimeters of each garden, because the area of a garden depends on the perimeter of the garden d. the students need to compare the areas of each garden, because the area of a garden does not depend on the perimeter of the garden

Explanation:

• Area and perimeter are two different concepts.
• Perimeter is the total length around a shape.
• Area is the measure of the space inside a shape.
• For example, a long - thin rectangle can have a large perimeter but a small area, while a square (with equal side lengths) can have a smaller perimeter but a larger area compared to some long - thin rectangles. So, to compare the space (area) to plant flowers, we need to compare areas directly as area does not depend on perimeter.

Answer:

D. The students need to compare the areas of each garden, because the area of a garden does not depend on the perimeter of the garden.