Question

Given segments uv, vw, and uw are midsegments. Of ts = 21, uw = 13, and vw = 19, what is the perimeter of \triangle△rst?

Answer 1

Using the triangle midsegment theorem, the perimeter of triangle RST is calculated as: 85 units.

What is the Triangle Midsegment Theorem?

The triangle midsegment theorem states that the length of each midsegment of a triangle is half the length of each corresponding third side of the triangle.

Given:

• TS = 21
• UW = 13
• VW = 19

Perimeter of triangle RST = TS + RS + RT

Find RS and RT using the midsegment theorem.

Thus:

RS = 2(UW)

RS = 2(13) = 26

RT = 2(VW)

RT = 2(19) = 38

Therefore:

Perimeter = 21 + 26 + 38 = 85 units.

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