Question

"Select all rectangles that are scaled copies of Rectangle Z. Rectangle Z has a length of 12 and width of 3.

Rectangle A has a length of 15 and a width of 30.
Rectangle B has a length of 36 and width of 9
Rectangle C has a length of 4 and width of 1.
Rectangle D has a length of 16.4 and width of 4.1
Rectangle E has a length of 18 and a width of 4
Rectangle F has a length of 24.8 and width of 7.2"

Answer 1

Only Rectangles B (36 by 9) and C (4 by 1) are scaled copies of Rectangle Z because they have the same length-to-width ratio of 4:1.

Step-by-step explanation:

To select all rectangles that are scaled copies of Rectangle Z, we must find rectangles with the same length-to-width ratio as Rectangle Z. Rectangle Z has dimensions of 12 units by 3 units. The scale factor between dimensions of two similar figures must be consistent for both length and width. Now, let's examine each rectangle provided:

• Rectangle A (15 by 30) is not a scaled copy because the ratio is 1:2, not 4:1 like Rectangle Z.
• Rectangle B (36 by 9) is a scaled copy because the ratio is 4:1, which is the same as Rectangle Z.
• Rectangle C (4 by 1) is a scaled copy because the ratio is 4:1, identical to Rectangle Z.
• Rectangle D (16.4 by 4.1) has a ratio that simplifies to approximately 4:1; however, it is not exact. So, for the purpose of this question, we will not consider it a perfect scaled copy.
• Rectangle E (18 by 4) does not have a 4:1 ratio and thus is not a scaled copy of Rectangle Z.
• Rectangle F (24.8 by 7.2) also does not have a 4:1 ratio, so it's not a scaled copy of Rectangle Z.

In conclusion, Rectangles B and C are the only scaled copies of Rectangle Z, as they share the same proportional dimensions.