Proportions & Scale Factors Quick Check
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Question
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
113
1 Start Fraction 1 over 3 End Fraction
123
1 Start Fraction 2 over 3 End Fraction
2
2
12
The correct answer is 2.
To find the scale factor, we need to compare the corresponding sides of the two triangles.
In the original triangle on the left, the longest side has a length of 18 inches and in the copy on the right, the corresponding longest side has a length of 30 inches.
To find the scale factor, we divide the length of the corresponding sides in the copy by the length of the corresponding sides in the original:
Scale factor = Length in copy / Length in original
Scale factor = 30 inches / 18 inches
Simplifying the fraction, we have:
Scale factor = 5/3
The scale factor Randee uses to create the copy on the right from the original on the left is 5/3. Therefore, the correct answer is:
1 Start Fraction 5 over 3 End Fraction
To find the scale factor used to create the copy of the triangle on the right from the original on the left, you need to compare corresponding sides of the two triangles.
In the original triangle on the left, the longest side has a length of 18 inches. In the copy on the right, the corresponding longest side is 30 inches. To find the scale factor, divide the length of the corresponding sides of the copy by the length of the corresponding sides of the original triangle.
In this case, the scale factor would be calculated as:
Scale factor = Length of corresponding side in copy / Length of corresponding side in original
Scale factor = 30 inches / 18 inches
Simplifying the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 6:
Scale factor = 5/3
Therefore, the scale factor used to create the copy on the right from the original on the left is 5/3.