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?
original triangle: 10 inches, 15 inches, 18 inches
new triangle: 36 inches, 20 inches, 30 inches
Responses
1 1/3
1 2/3
1/2
2
To find the scale factor, we can compare the corresponding side lengths of the triangles. The corresponding side lengths are as follows:
Original triangle: 10 inches, 15 inches, 18 inches
New triangle: 36 inches, 20 inches, 30 inches
Comparing the first side lengths, 10 inches and 36 inches, we can see that the scale factor is 36/10 = 3.6.
Comparing the second side lengths, 15 inches and 20 inches, we can see that the scale factor is 20/15 = 1.33 (rounded to two decimal places).
Comparing the third side lengths, 18 inches and 30 inches, we can see that the scale factor is 30/18 = 1.67 (rounded to two decimal places).
Since the scale factor should be the same for all side lengths, we can take the average of the two scale factors found for the second and third side lengths:
(1.33 + 1.67) / 2 = 1.5
Therefore, Randee uses a scale factor of 1.5 to create the copy on the right from the original on the left.