The length of the smaller triangle has 10in , 15in, 18in,
and the larger triangle has 20 in, 30 in, and 36 in,
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?
To find the scale factor, we need to compare the corresponding sides of both triangles.
For the smaller triangle:
Length of the corresponding side in the copy = 10 cm
Length of the corresponding side in the original = 10 in = 25.4 cm (since 1 inch = 2.54 cm)
Scale factor for the smaller triangle = Length in copy / Length in original = 10 / 25.4 = 0.3937
For the larger triangle:
Length of the corresponding side in the copy = 20 cm
Length of the corresponding side in the original = 20 in = 50.8 cm (since 1 inch = 2.54 cm)
Scale factor for the larger triangle = Length in copy / Length in original = 20 / 50.8 = 0.3937
Therefore, Randee uses a scale factor of 0.3937 to create the copy on the right from the original on the left.
To determine the scale factor, we need to compare the corresponding sides of the smaller and larger triangles. Let's convert the lengths from inches to centimeters first.
1 inch is equal to 2.54 centimeters. Therefore, the lengths in centimeters are as follows:
Smaller triangle:
Side 1: 10 inches * 2.54 cm/inch = 25.4 cm
Side 2: 15 inches * 2.54 cm/inch = 38.1 cm
Side 3: 18 inches * 2.54 cm/inch = 45.7 cm
Larger triangle:
Side 1: 20 inches * 2.54 cm/inch = 50.8 cm
Side 2: 30 inches * 2.54 cm/inch = 76.2 cm
Side 3: 36 inches * 2.54 cm/inch = 91.4 cm
Now, let's find the scale factor by comparing the corresponding sides:
Scale factor = (Length of side in larger triangle) / (Length of side in smaller triangle)
For the first side:
Scale factor = 50.8 cm / 25.4 cm = 2
For the second side:
Scale factor = 76.2 cm / 38.1 cm = 2
For the third side:
Scale factor = 91.4 cm / 45.7 cm = 2
Since all three sides have the same scale factor, we can conclude that Randee used a scale factor of 2 to create the copy on the right from the original on the left.
To determine the scale factor, we need to compare the corresponding sides of the two triangles.
In the smaller triangle, the lengths are given as 10in, 15in, and 18in. Before we can compare the lengths, we need to convert them from inches to centimeters.
1 inch is equal to 2.54 centimeters, so we can multiply each length by 2.54 to convert them.
The smaller triangle in centimeters becomes: 10 in * 2.54 cm/in = 25.4 cm, 15 in * 2.54 cm/in = 38.1 cm, and 18 in * 2.54 cm/in = 45.72 cm.
Now, let's compare the corresponding sides with the larger triangle. The lengths of the larger triangle are given as 20 in, 30 in, and 36 in. Similarly, we convert these lengths to centimeters.
The larger triangle in centimeters becomes: 20 in * 2.54 cm/in = 50.8 cm, 30 in * 2.54 cm/in = 76.2 cm, and 36 in * 2.54 cm/in = 91.44 cm.
To calculate the scale factor, we can compare the corresponding sides of the triangles:
For the first pair of sides:
25.4 cm / 50.8 cm = 0.5
For the second pair of sides:
38.1 cm / 76.2 cm = 0.5
For the third pair of sides:
45.72 cm / 91.44 cm = 0.5
Since all the ratios are equal to 0.5, we can determine that the scale factor used to create the copy on the right from the original on the left is 0.5.