+713 In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.
+975 To start, if all sides of a quadrilateral are equal and the diaganols are equal, then we defintely have a square.
The square of diagonal of a square is equal to 2 times the square of the sidelegnth. We have
\(2PQ^2 = (\sqrt2)^2 \\ 2PQ^2 = 2 \\ PQ^2 = 1 \\ PQ = 1\)
The perimeter is just \(1+1+1+1 = 4\)
So 4 is the answer.
(We could check. The diagonal of a square with sidelength 1 is actually sqrt2, so we are clear!)
Thanks! :)
+975 To start, if all sides of a quadrilateral are equal and the diaganols are equal, then we defintely have a square.
The square of diagonal of a square is equal to 2 times the square of the sidelegnth. We have
\(2PQ^2 = (\sqrt2)^2 \\ 2PQ^2 = 2 \\ PQ^2 = 1 \\ PQ = 1\)
The perimeter is just \(1+1+1+1 = 4\)
So 4 is the answer.
(We could check. The diagonal of a square with sidelength 1 is actually sqrt2, so we are clear!)
Thanks! :)
