Fill in the blank question.

Question

Jim has a yard sign measuring 45 centimeters by 60 centimeters for his mayoral campaign. He wants to use the same image for a sticker. Jim reduces the image by a scale factor of 15, and to print the sticker, he reduces the second image by a scale factor of 13.

What are the dimensions of the sticker? Write the smaller dimension first and the larger dimension second.

Answer 1

To find the dimensions of the sticker, we first need to reduce the original dimensions of the yard sign (45 cm by 60 cm) by a scale factor of 15, and then further reduce the resulting dimensions by a scale factor of 13.

1. Reduce by a scale factor of 15:

   • Smaller dimension: \( 45 , \text{cm} \div 15 = 3 , \text{cm} \)
   • Larger dimension: \( 60 , \text{cm} \div 15 = 4 , \text{cm} \)

   After this step, the dimensions are 3 cm and 4 cm.

2. Reduce by a scale factor of 13:

   • Smaller dimension: \( 3 , \text{cm} \div 13 = \frac{3}{13} , \text{cm} \)
   • Larger dimension: \( 4 , \text{cm} \div 13 = \frac{4}{13} , \text{cm} \)

Thus, the final dimensions of the sticker are \( \frac{3}{13} , \text{cm} \) (smaller dimension) and \( \frac{4}{13} , \text{cm} \) (larger dimension).

Therefore, the dimensions of the sticker are:

\(\frac{3}{13} , \text{cm}, \frac{4}{13} , \text{cm}\).

Answer 2

Are the reduced images similar to the original? Write yes or no.

Answer 3

Yes.

Answer 4

What are the dimensions of the sticker?

Answer 5

Let's recalculate the dimensions of the sticker based on the original dimensions of the yard sign (45 cm by 60 cm) and the provided scale factors.

1. Reduce by a scale factor of 15:

   • Smaller dimension: \( 45 , \text{cm} \div 15 = 3 , \text{cm} \)
   • Larger dimension: \( 60 , \text{cm} \div 15 = 4 , \text{cm} \)

   Now, the dimensions are 3 cm and 4 cm.

2. Reduce this image by a scale factor of 13:

   • Smaller dimension: \( 3 , \text{cm} \div 13 = \frac{3}{13} , \text{cm} \)
   • Larger dimension: \( 4 , \text{cm} \div 13 = \frac{4}{13} , \text{cm} \)

Thus, the dimensions of the sticker are:

\(\frac{3}{13} , \text{cm}, \frac{4}{13} , \text{cm}\).

Please note that if the first reduction was indeed the intended operation, the answer holds true. However, if the original dimensions were to first reduce the height 45 cm by a factor of 15 and then the width of 60 cm also by a factor of 15, it would lead to different dimensions. Let me know if you would like that calculation instead!