Triangle TRS is rotated about point X, resulting in triangle BAC. Triangle T R S is rotated about point X to form triangle B A C. The lengths of sides T R and A B are congruent, the lengths of sides A C and R S are congruent, and the lengths of sides T S and B C are congruent. If AB = 10 ft, AC = 14 ft, and BC = 20 ft, what is RS? 10 ft 14 ft 20 ft 24 ft

The length of side length RS 14 ft

Rotation involves moving a shape in a circular motion about a fixed point i.e. when a shape is rotated, it must be rotated about a point.

The given parameters are:

Given that:

And we have:

Substitute 14 for AC in the above equation

Hence, the length of RS 14 ft

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RS = 14 ft

Explanation:

Rotation is a type of transformation that changes the orientation of a given shape or figure without any effects to its dimensions.

Thus, rotating ΔTRS about point X would not change the value of its sides to produce ΔBAC. So that;

  /AB/ = /TR/

  /AC/ = /RS/

  /BC/ = /TS/

The two given triangles are congruent and they have the same values of sides.

Therefore,

  /AC/ = /RS/ = 14 feet

Thus, /RS/ = 14 ft

associative property of addition