Alyssa Z.

asked • 03/03/21

what is the perimeter of △XYZ?

Assume that X, Y, and Z are midpoints of the sides of △RST. If the perimeter (sum of the lengths of all three sides) of △RST is 40, what is the perimeter of △XYZ?

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Inactive Tutor answered • 03/03/21

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I agree with Raymond, the midpoints set up three parallelograms, in my drawing, TZXY, RXYZ, AND SYZX are parallelograms (I checked slopes with coordinate geometry). It becomes clear ZY=RS/2, XY=RT/2 and ZX=ST/2.

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Alssya, it is also a 100% true thing that if any quadrilateral has it's sides mid-pointed and those mid-points connected to make an "inside quadrilateral,"[[[[[[[]]]]]]] that "inner quadrilateral" is a parallelogram. The proof is easy kind of with coordinate geometry. And it is fun to show off with. Draw any quadrilateral, estimate mid points and mark. connect midpoints and whala it is a parallelogram.
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03/04/21

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