Question

triangle wxy is formed by connecting the midpoints of the side of triangle tuv. the lengths of the sides of triangle wxy are shown. find the perimeter of triangle tuv. figures not necessarily drawn to scale.

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of a mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side of the triangle.
If \(WX = 4\), then the side of \(\triangle TUV\) parallel to \(WX\) (say \(TV\)) has length \(2\times4=8\).
If \(XY = 5\), then the side of \(\triangle TUV\) parallel to \(XY\) (say \(TU\)) has length \(2\times5 = 10\).
If \(YW=4\), then the side of \(\triangle TUV\) parallel to \(YW\) (say \(UV\)) has length \(2\times4=8\).

Step2: Calculate the perimeter of \(\triangle TUV\)

The perimeter \(P\) of a triangle is \(P=a + b + c\), where \(a\), \(b\), and \(c\) are the side lengths of the triangle.
For \(\triangle TUV\), \(a = 8\), \(b = 10\), \(c = 8\).
\(P=8 + 10+8\)

Answer:

\(26\)