Triangle MNP is dilated to obtain triangle QRS. Using the same scale factor, triangle QRS is dilated to obtain triangle TUV. MN 30 meters, NP 25 meters, PM 25 meters, and QR 42 meters. What is the perimeter, in meters, of triangle TUV?

Question

Mathematics

Cox

14 April, 09:50

Triangle MNP is dilated to obtain triangle QRS. Using the same scale factor, triangle QRS is dilated to obtain triangle TUV. MN 30 meters, NP 25 meters, PM 25 meters, and QR 42 meters. What is the perimeter, in meters, of triangle TUV?

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Reid · Answer 1

Answer: The perimeter of triangle TUV is 156.8 meters.

First, we need to find the scale factor that is used in the dilations. MN goes from 30 to 42 when it becomes side QR. Dividing 42 by 30 gives us a scale factor of 1.4.

The perimeter of triangle MNP is 80. Now, we have to multiply that by 1.4 twice to get to the perimeter of triangle TUV.

80 x 1.4 x 1.4 = 156.8