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

2
2

12
Start Fraction 1 over 2 End Fraction

113
1 Start Fraction 1 over 3 End Fraction

123

Answer 1

To determine the scale factor that Randee uses to create the copy of the triangle, we need to compare the side lengths of the two triangles.

Left Triangle:

• Base: 18 inches
• Other sides: 10 inches and 15 inches

Right Triangle:

• Sides: 30 inches, 36 inches, and 20 inches

All lengths will be converted to centimeters. However, as both sets of measurements are given in inches and do not state a specific multiplication or conversion to centimeters, we will calculate the scale factor based on their ratios directly.

The corresponding side lengths of the triangles that can be compared should be matched appropriately. The longest side of the first triangle (let’s assume the base 18 inches is not the longest since it’s specified in position) isn't given directly, but based on the context of the question we can calculate:

1. Calculating the longest side of the first triangle: The longest side can potentially be calculated with the sides given (the triangle inequality); however, for simplicity, since we’re looking for a ratio, we can consider the longest side noticed in the context.

2. If we look closely at dimensions: When comparing the longest sides, given as 30 inches for the right triangle, it would logically relate to a appropriate length from the first.

Calculate the scale factor using the longest sides:

Assuming the lengths (for simplicity):

• First Triangle --> Longest side can assumed as 18 inches (baseline)
• Second Triangle --> Longest side is 36 inches

Scale factor: To get the scale factor, we can divide the lengths of the corresponding sides:

Scale Factor = Longest side of the second triangle / Longest side of the first triangle = 36 inches / 18 inches = 2

So, the scale factor used to create the copy on the right from the original on the left is 2.