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

Algebra ->  Points-lines-and-rays -> SOLUTION: In (SQUARE SYMBOL - rectangle?) ABCD, P, Q, R, and S are mid-points of the sides. The perimeter of (SQUARE SYMBOL - rectangle?) ABCD is 40, and AC = 17, BD = 17. What is the perime      Log On


   

Question 1011960: In (SQUARE SYMBOL - rectangle?) ABCD, P, Q, R, and S are mid-points of the sides. The perimeter of (SQUARE SYMBOL - rectangle?) ABCD is 40, and AC = 17, BD = 17. What is the perimeter of (SQUARE SYMBOL - rectangle?)PQRS.
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Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
Similar problems were solved many times in few days.

The answer is: 17 + 17 = 34.

The info about 40 is excessive.

The idea of solution is that the points P, Q, R and S are vertices of a parallelogram.
The sides of this parallelogram are mid-lines of triangles based on diagonals,
and their dimensions are half measures of diagonals of the original quadrilateral.

See these lessons in this site:
Midpoints of a quadrilateral are vertices of the parallelogram and
The line segment joining the midpoints of two sides of a triangle.