Determine if the measurements given represent the dimensions of a triangle that is similar to triangle QRS.
10 cm, 14 cm, 18 cm
6 cm, 8 cm, 10 cm
40 cm, 56 cm, 72 cm
To determine if the measurements given represent the dimensions of a triangle that is similar to triangle QRS, we need to compare the ratios of the corresponding sides.
First, let's list the ratios of the corresponding sides of each triangle:
Triangle QRS: QR/QS = RS/QR = QS/RS
1. For the measurements 10 cm, 14 cm, 18 cm:
10/14 = 0.71
14/18 = 0.78
18/10 = 1.8
These ratios do not match the ratios of triangle QRS, so this triangle is not similar to triangle QRS.
2. For the measurements 6 cm, 8 cm, 10 cm:
6/8 = 0.75
8/10 = 0.8
10/6 = 1.67
These ratios do match the ratios of triangle QRS, so this triangle is similar to triangle QRS.
3. For the measurements 40 cm, 56 cm, 72 cm:
40/56 = 0.71
56/72 = 0.78
72/40 = 1.8
These ratios do match the ratios of triangle QRS, so this triangle is similar to triangle QRS.
Therefore, the measurements 6 cm, 8 cm, 10 cm and 40 cm, 56 cm, 72 cm represent triangles that are similar to triangle QRS.