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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.

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

2
2

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

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

1/2

1 answer

To determine the scale factor that Randee used to create the copy of the original triangle, we need to compare the corresponding sides of the two triangles.

For the first triangle (original), the sides are 10 inches, 15 inches, and 18 inches.

For the second triangle (copy), the lengths are given as 20 inches, 30 inches, and 36 inches.

To find the scale factor, we can compare the corresponding sides:

  1. Compare the longest sides:

    • Original longest side: 18 inches
    • Copy longest side: 36 inches
    • Scale factor for longest side: \( \frac{36}{18} = 2 \)

  2. Compare the second longest sides:

    • Original second side: 15 inches
    • Copy second side: 30 inches
    • Scale factor for second side: \( \frac{30}{15} = 2 \)

  3. Compare the shortest sides:

    • Original shortest side: 10 inches
    • Copy shortest side: 20 inches
    • Scale factor for shortest side: \( \frac{20}{10} = 2 \)

Since all corresponding sides have the same scale factor of 2, we conclude that the scale factor Randee used to create the copy is 2.

The answer is 2.