+0  
 
0
1
1
avatar+620 

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.

 Jun 1, 2024

Best Answer 

 #1
avatar+806 
+1

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! :)

 Jun 1, 2024
 #1
avatar+806 
+1
Best Answer

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! :)

NotThatSmart Jun 1, 2024

0 Online Users