the original photo is a rectangle that is 4 inches wide and 6 inches high. Can it be changed to a similar rectangle with the given measurements (in inches)?
A.) 8by12 B.)9by11 C.)6by9 D.) 3by4.5
they are all different questions
The ratio is 2 to 3. Do any of the other dimensions have the same ratio?
To determine whether two rectangles are similar, we need to compare their corresponding sides and see if the ratios are the same.
Let's calculate the ratios of the sides of the original rectangle:
Width ratio = Original width / Original height = 4 / 6 = 2/3
Height ratio = Original height / Original width = 6 / 4 = 3/2
Now, let's calculate the ratios of the sides of the possible rectangles:
A) 8 by 12:
Width ratio = 8 / 12 = 2/3
Height ratio = 12 / 8 = 3/2
B) 9 by 11:
Width ratio = 9 / 11 ≈ 0.818
Height ratio= 11 / 9 ≈ 1.222
C) 6 by 9:
Width ratio = 6 / 9 = 2/3
Height ratio= 9 / 6 = 1.5
D) 3 by 4.5:
Width ratio = 3 / 4.5 ≈ 0.667
Height ratio = 4.5 / 3 = 1.5
Comparing the ratios, we can see that:
- Option A) 8 by 12: The ratios match, so it is a similar rectangle.
- Option B) 9 by 11: The ratios do not match, so it is not a similar rectangle.
- Option C) 6 by 9: The ratios match, so it is a similar rectangle.
- Option D) 3 by 4.5: The ratios match, so it is a similar rectangle.
Therefore, the possible rectangles that are similar to the original rectangle are:
A) 8 by 12
C) 6 by 9
D) 3 by 4.5