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 10 in, 15, in, 18 in, 20 in, 30 in, 36 in.
To find the scale factor, we need to compare the corresponding sides of the two triangles.
Let's call the original triangle ABC and the copy triangle DEF.
We are given the following lengths for the corresponding sides:
AB = 10 in
BC = 15 in
AC = 18 in
DE = 20 in
EF = 30 in
DF = 36 in
To find the scale factor, we can compare the lengths of AB and DE:
scale factor = DE / AB
scale factor = 20 in / 10 in
scale factor = 2
Therefore, Randee uses a scale factor of 2 to create the copy triangle.
To determine the scale factor, we need to compare the corresponding side lengths of the two triangles.
Let's denote the original triangle's side lengths as a, b, and c, and the corresponding side lengths of the copy as A, B, and C.
We can calculate the scale factor (k) between the two triangles by dividing the corresponding side lengths:
k = A/a = B/b = C/c
Let's calculate the scale factor for each set of side lengths given:
Set 1: a = 10 in, b = 15 in, c = 18 in
A = 10 in, B = 15 in, C = 18 in
k = A/a = 10/10 = 1
The scale factor is 1.
Set 2: a = 10 in, b = 15 in, c = 18 in
A = 20 in, B = 30 in, C = 36 in
k = A/a = 20/10 = 2
The scale factor is 2.
Therefore, based on the sets of side lengths given, we have two scale factors: 1 and 2.
To determine the scale factor, we need to compare the corresponding side lengths of the two triangles. Let's denote the original triangle as Triangle A and the copy as Triangle B.
1. Start by comparing the corresponding side lengths of Triangle A and Triangle B.
- The length of one side in Triangle A is 10 inches, while the corresponding side in Triangle B is 18 inches.
- This tells us that the scale factor from Triangle A to Triangle B is 18/10 or 1.8.
2. Repeat the process for the other corresponding side lengths:
- Length in Triangle A: 15 inches; Length in Triangle B: ? (Let's call it x)
Scale factor: x/15 = ?
- Length in Triangle A: 20 inches; Length in Triangle B: ? (Let's call it y)
Scale factor: y/20 = ?
3. Use the formula for the scale factor:
Scale factor = Length in Triangle B / Length in Triangle A
4. Now, let's calculate the missing side lengths using the scale factor:
- Length in Triangle A: 15 inches; Length in Triangle B: x
Scale factor: x/15 = ?
Cross-multiply: x = ? * 15
- Length in Triangle A: 20 inches; Length in Triangle B: y
Scale factor: y/20 = ?
Cross-multiply: y = ? * 20
5. Repeat the process for the remaining side lengths (30 inches and 36 inches) to find their respective scale factors.
By following these steps, you can determine the scale factor for each triangle based on the given side lengths.