Use the image to answer the question.
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
12
Start Fraction 1 over 2 End Fraction
1 Start Fraction 2 over 3 End Fraction
2
2
113
To find the scale factor, we can compare the lengths of corresponding sides in the two triangles.
In the first triangle, the longest side (the baseline) has a length of 18 inches. In the second triangle, the longest side is also the baseline, but it has a length of 30 inches. The ratio of the lengths of the baselines is:
30/18 = 5/3
So, the scale factor for the baseline is 5/3.
Now, let's compare the lengths of the two shorter sides. In the first triangle, the shorter side has a length of 10 inches, while in the second triangle, the corresponding side has a length of 20 inches. The ratio of the lengths of these sides is:
20/10 = 2/1
So, the scale factor for the shorter side is 2/1.
Since we have two different scale factors, we can take the average to find the overall scale factor:
(5/3 + 2/1) / 2 = (5/3 + 6/3) / 2 = 11/3 / 2 = 11/6
Therefore, Randee uses a scale factor of 11/6 to create the copy of the triangle on the right from the original triangle on the left.