The Ratio Of The Perimeters Of Two Similar Triangles Are2 Is To 6. What Is The Corresponding Side Of The Second Triangle, If One Side Of The First Tri

the ratio of the perimeters of two similar triangles are2 is to 6. what is the corresponding side of the second triangle, if one side of the first triangle is 3 in?

Answer:

The corresponding side of the second triangle measures 9 inches.

Step-by-step explanation:

Triangle Similarities Theorem on the triangles side and its perimeter:

In similar triangles, the ratios of the corresponding sides is called the scale factor.  

The scale factor of similar triangles is the ratio of their perimeters.

Therefore, in ΔABC and ΔDEF:

ΔABC/ΔDEF = AB/DE

Where the ratio of perimeters of ΔABC to ΔDEF is 2:6, and side AB is 3 in.

Equation:

Let side DE be x.

2/6 = 3:x

2x = (3)(6)

2x/2 = 18/2

x = 9

The corresponding side of the second triangle measures 9 inches.


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