An illustration shows two triangles positioned differently. The first triangle has its longest side along the baseline. The second triangle has its longest side in the upper left, and the triangle is tilted upward to the right. The first triangle has a base of 18 inches and sides as 10 inches and 15 inches. The second triangle shows three sides as 30 inches, 36 inches, and 20 inches.

Question

Randee draws these two triangles with lengths given in centimeters. What scale factor does she use to create the copy on the right from the original on the left?

(1 point)
Responses

1/2
Start Fraction 1 over 2 End Fraction

1 2/3
1 Start Fraction 2 over 3 End Fraction

1 1/3
1 Start Fraction 1 over 3 End Fraction

2

Answer 1

To determine the scale factor used by Randee to create the second triangle from the first triangle, we first need to convert the dimensions from inches to centimeters. The dimensions provided for both triangles are as follows:

First Triangle (in inches):

• Base: 18 inches
• Side 1: 10 inches
• Side 2: 15 inches

Second Triangle (in inches):

• Side 1: 30 inches
• Side 2: 36 inches
• Side 3: 20 inches

Next, we need to establish the scale factor between the corresponding sides of both triangles.

1. Convert the side lengths from inches to centimeters. Since \(1 , \text{inch} \approx 2.54 , \text{cm}\), we can multiply each side by 2.54:

   First Triangle (in cm):

   • Base: \( 18 \times 2.54 \approx 45.72 , \text{cm} \)
   • Side 1: \( 10 \times 2.54 \approx 25.4 , \text{cm} \)
   • Side 2: \( 15 \times 2.54 \approx 38.1 , \text{cm} \)

   Second Triangle (in cm) (using prior ratios or scale):

   • Side 1: \( 30 \times 2.54 \approx 76.2 , \text{cm} \)
   • Side 2: \( 36 \times 2.54 \approx 91.44 , \text{cm} \)
   • Side 3: \( 20 \times 2.54 \approx 50.8 , \text{cm} \)

2. Now we find the scale factor by taking the ratio of corresponding sides.

Let's compare the longest sides of both triangles:

• The longest side of the first triangle (15 inches = 38.1 cm) to the longest side of the second triangle (36 inches = 91.44 cm):

\[ \text{Scale Factor} = \frac{\text{Length of Second Triangle Side}}{\text{Length of First Triangle Side}} = \frac{91.44 , \text{cm}}{38.1 , \text{cm}} \approx 2.4 \]

Doing this for the other sides (using 10 inches = 25.4 cm):

• \( 30 \text{ inches} / 10 \text{ inches} = 3 \)
• \( 36 \text{ inches} / 15 \text{ inches} = 2.4 \) (to approximate each)

However, since numbers may represent in the same overall ratio, we utilize a ratio scale.

Since 15 is to 36 like 10 is to 30.

Finally concluding that henceforth intended transforms or approximations would be required to focus correctly on scalings and aspect interactions over side interactions.

The best approximated answer based on ratios and direct calculations leads us toward the established 2.

The result is that the scale factor Randee used to create the copy is 2.