There are 3 gardens below. They are all joined. Garden A and C are are perfect squares. A is 121 m2 and C is 169 m2. What is the area of garden B? Label all the dimensions and then find the perimeter of the entire three gardens that are joined together?
All I know is that 11x11 = 121 and 13x13 = 169
To find the area of garden B, we can subtract the areas of gardens A and C from the total area.
The total area of the three joined gardens is 121 m² + 169 m² = 290 m².
Since garden A is a perfect square with an area of 121 m², its side length can be found by taking the square root of the area: √121 = 11m. Let's label the side length of garden A as A_side.
Similarly, garden C is a perfect square with an area of 169 m², so its side length can be found by taking the square root of the area: √169 = 13m. Let's label the side length of garden C as C_side.
The total area of the three gardens is equal to the sum of the areas of gardens A, B, and C:
A_area + B_area + C_area = 290 m²
Since garden A and garden C are perfect squares, we can say that garden B is also a square, with a side length equal to the difference between the side lengths of garden A and C:
B_side = C_side - A_side
Now, let's find the side length of garden B:
B_side = 13m - 11m = 2m
The area of a square is found by multiplying the side length by itself, so the area of garden B is:
B_area = B_side × B_side = 2m × 2m = 4 m²
Therefore, the area of garden B is 4 m².
To find the perimeter of the entire three joined gardens, we need to add up the perimeters of gardens A, B, and C.
The perimeter of a square is found by multiplying the side length by 4, so the perimeter of garden A is:
A_perimeter = A_side × 4 = 11m × 4 = 44m
Similarly, the perimeter of garden C is:
C_perimeter = C_side × 4 = 13m × 4 = 52m
The perimeter of garden B is also:
B_perimeter = B_side × 4 = 2m × 4 = 8m
To find the perimeter of the three joined gardens, we add up the perimeters:
Total_perimeter = A_perimeter + B_perimeter + C_perimeter
Total_perimeter = 44m + 8m + 52m
Total_perimeter = 104m
Therefore, the perimeter of the entire three joined gardens is 104 meters.
To find the area of garden B, we need to determine its dimensions. Since garden A is a perfect square with an area of 121 m2 and garden C is a perfect square with an area of 169 m2, we can calculate the lengths of their sides.
The length of each side of garden A can be found by taking the square root of its area. So, the length of the sides of garden A is √121 = 11 m.
Similarly, the length of each side of garden C is √169 = 13 m.
Now, since gardens A and C are joined, the length of garden B is the difference between the sides of gardens C and A. Therefore, the length of each side of garden B is 13 m - 11 m = 2 m.
To find the area of garden B, we multiply the length of one side by itself. So the area of garden B is 2 m × 2 m = 4 m2.
Now, to find the perimeter of the three joined gardens, we need to add up the lengths of all the sides.
Garden A has four sides of equal length, each measuring 11 m. So the total length of the sides of garden A is 4 × 11 m = 44 m.
Garden B has four sides of equal length, each measuring 2 m. So the total length of the sides of garden B is 4 × 2 m = 8 m.
Garden C has four sides of equal length, each measuring 13 m. So the total length of the sides of garden C is 4 × 13 m = 52 m.
Now, we add up the lengths of all sides to find the perimeter of the three gardens: 44 m + 8 m + 52 m = 104 m.
Therefore, the area of garden B is 4 m2 and the perimeter of the three joined gardens is 104 m.