Julia drew this rectangle on grid paper. Which rectangle has the same area but a greater perimeter than Julia's rectangle?
A.
A square is divided into four rows of four equal squares.
B.
A rectangle is divided into 2 rows of 10 equal squares.
C.
A rectangle is divided into 3 rows of 6 equal squares.
D.
A rectangle is divided into 3 rows of 5 equal squares.
C. A rectangle is divided into 3 rows of 6 equal squares.
To determine which rectangle has the same area but a greater perimeter than Julia's rectangle, we need to compare the areas and perimeters of the options given.
Option A: A square divided into four rows of four equal squares. Since it is a square, all four sides are equal in length.
Option B: A rectangle divided into 2 rows of 10 equal squares. To find the area, we can multiply the length by the width. The length is 2 rows, which means it has a length of 2 squares. The width is 10 squares. Therefore, the area is 2 x 10 = 20 square units.
Option C: A rectangle divided into 3 rows of 6 equal squares. Similar to Option B, we can find the area by multiplying the length by the width. The length is 3 rows, or 3 squares, and the width is 6 squares. Therefore, the area is 3 x 6 = 18 square units.
Option D: A rectangle divided into 3 rows of 5 equal squares. Again, we can find the area by multiplying the length by the width. The length is 3 rows, or 3 squares, and the width is 5 squares. Therefore, the area is 3 x 5 = 15 square units.
Comparing the areas of the options, we have:
Option A: Area unknown
Option B: Area = 20 square units
Option C: Area = 18 square units
Option D: Area = 15 square units
Since we do not know the area of Option A, we cannot determine if it has the same area as Julia's rectangle or not.
Now, let's compare the perimeters of the options:
Option A: A square divided into four rows of four equal squares. Since it is a square, all four sides are equal in length.
Option B: A rectangle divided into 2 rows of 10 equal squares. The perimeter of a rectangle is calculated by adding up the lengths of all four sides. The length is 2 rows, or 2 squares, and the width is 10 squares. Therefore, the perimeter is 2 + 2 + 10 + 10 = 24 units.
Option C: A rectangle divided into 3 rows of 6 equal squares. The length is 3 rows, or 3 squares, and the width is 6 squares. Therefore, the perimeter is 3 + 3 + 6 + 6 = 18 units.
Option D: A rectangle divided into 3 rows of 5 equal squares. The length is 3 rows, or 3 squares, and the width is 5 squares. Therefore, the perimeter is 3 + 3 + 5 + 5 = 16 units.
Comparing the perimeters of the options, we have:
Option A: Perimeter unknown
Option B: Perimeter = 24 units
Option C: Perimeter = 18 units
Option D: Perimeter = 16 units
Based on the information provided, we cannot determine which rectangle has the same area but a greater perimeter than Julia's rectangle. The areas and perimeters of Options A would need to be known to make a clear comparison.