SOLUTION: In (square symbol?) ABCD, P, Q, R, and S are mid-points of the sides. The perimeter of (square symbol?) ABCD is 40, and AC = 17, BD = 11. What is the perimeter of (square symbol?)

Question 1012062: In (square symbol?) ABCD, P, Q, R, and S are mid-points of the sides. The perimeter of (square symbol?) ABCD is 40, and AC = 17, BD = 11. What is the perimeter of (square symbol?) PQRS.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The rectangular symbol means "quadrilateral".

Construct the diagonals of your original quadrilateral, namely the segments AC and BD.

Note that the segment AC forms two triangles, ADC and ABC. By the Midline Theorem, the segment that connects the midpoints of two sides of a triangle is parallel to and half the measure of the third side. Hence, each of the segments SP and QR are half the measure of AC. Likewise, each of QP and RS are half the measure of BD.

The rest is just arithmetic.

John

My calculator said it, I believe it, that settles it

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