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Question

The triangle, ΔXYZ, shown above has sides of lengths x,y and z inches and is not a right angled triangle. Let X be the image of X when the triangle is reflected across ¯¯¯¯¯¯¯¯YZ. Find the correct expression for the perimeter, in inches, of quadrilateral X,YXZ.
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A
2(y+z)+x
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B
2(x+y+z)
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C
2(x+y)
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D
2(x+z)
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E
2(y+z)
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Solution

The correct option is D 2(y+z)
Reflecting the triangle over YZ will create a parallelogram with the vertices X, Y, X (X prime), and Z.
The perimeter of a polygon is the sum total of the sides.
In this case, the sides will sum to: z+y+z+y.
Factoring this will give us: 2z+2y.
Factoring again will leave 2(z+y) or 2(y+z).

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