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
2
2
12
Start Fraction 1 over 2 End Fraction
113
1 Start Fraction 1 over 3 End Fraction
123
1 Start Fraction 2 over 3 End Fraction
To find the scale factor, we need to compare the corresponding sides of the two triangles.
In the original triangle (on the left):
Longest side = 18 inches
In the copied triangle (on the right):
Longest side = 30 centimeters
To find the scale factor, we can take the ratio of the corresponding sides:
Scale factor = length of longest side in the copy / length of longest side in the original
Scale factor = 30 centimeters / 18 inches
Since we need the lengths to be in the same unit, let's convert inches to centimeters. There are 2.54 centimeters in 1 inch.
Scale factor = (30 centimeters / 18 inches) * (2.54 centimeters / 1 inch)
Scale factor = (30 * 2.54) centimeters / (18 * 1) inches
Scale factor = 76.2 centimeters / 18 inches
Simplifying the fraction, we get:
Scale factor = 4.2333...
So, Randee used a scale factor of approximately 4.2 to create the copy on the right from the original on the left.
choose a option from my qustoin
Based on the given options, the correct answer is:
123
1 Start Fraction 2 over 3 End Fraction
To answer this question, we need to compare the lengths of corresponding sides in the two triangles. Let's compare the longest side of the original triangle with the longest side of the copy.
In the original triangle, the longest side has a length of 18 inches. In the copy, the longest side has a length of 30 inches.
To determine the scale factor, we divide the length of the longest side in the copy by the length of the longest side in the original:
Scale factor = Length of longest side in copy / Length of longest side in original
Scale factor = 30 inches / 18 inches
To convert the lengths from inches to centimeters, we need to know the conversion factor. Let's assume 1 inch is equal to 2.54 centimeters.
So, the lengths become:
Length of longest side in copy = 30 inches * 2.54 centimeters/inch
Length of longest side in copy = 76.2 centimeters
Length of longest side in original = 18 inches * 2.54 centimeters/inch
Length of longest side in original = 45.72 centimeters
Now, let's calculate the scale factor in centimeters:
Scale factor = 76.2 centimeters / 45.72 centimeters
Scale factor ≈ 1.6667
Therefore, the scale factor Randee used to create the copy on the right from the original on the left is approximately 1.6667.