The dimensions of rectangle A are three times the dimensions of rectangle B. The area of rectangle A is 450 cm2.
What is the area of rectangle B?
Let the dimensions of rectangle B be length = L cm and width = W cm.
Since the dimensions of rectangle A are three times the dimensions of rectangle B, we have:
Length of A = 3L
Width of A = 3W
We are given that the area of rectangle A is 450 cm²:
Area of A = Length of A * Width of A
450 = 3L * 3W
450 = 9LW
Now, we need to find the area of rectangle B:
Area of B = Length of B * Width of B
Area of B = L * W
Since the area of rectangle A is 450 cm², we can substitute L = 3W into the equation to find the area of rectangle B:
450 = 9LW
450 = 9(3W)W
450 = 27W²
W² = 450 / 27
W² = 16.67
W ≈ √16.67
W ≈ 4.08
Now that we have the width of rectangle B, we can find the length of rectangle B:
L = 3W
L = 3(4.08)
L ≈ 12.24
Finally, we can find the area of rectangle B:
Area of B = L * W
Area of B ≈ 12.24 * 4.08
Area of B ≈ 49.9 cm²
Therefore, the area of rectangle B is approximately 49.9 cm².