A) It is a contraction; the scale factor is 3/4. B) AR = 2.2 cm. C) TN = 9.6 cm. D) The scale factors for the areas would be 16/9.
Explanation A) It is a contraction because it gets smaller. To find the scale factor, compare AN to RI: 12/16, which reduces to 3/4.
B) First we must find the length of TR. We know that TA = 0.75TR. We also know that TA = 6.6:
6.6 = 0.75TR
Divide both sides by 0.75: 6.6/0.75 = 0.75TR/0.75 8.8 = TR
We also know that AR = TR - TA: AR = 8.8 - 6.6 AR = 2.2.
C) The side splitter theorem leads us to the proportion TA/AR = TN/NI
Plugging in what we know, we have: 6.6/2.2 = TN/3.2
Cross multiply: 6.6*3.2 = 2.2TN 21.12 = 2.2TN
Divide both sides by 2.2: 21.12/2.2 = 2.2TN/2.2 9.6 = TN
D) The ratio of the area would be the square of the ratio of the sides. The ratio of side TR to TA is 4/3; therefore the ratio of their areas would be 16/9.