If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig

Looks scary if you're inclined to hate geometry like myself, but quite simple when you remember rules and take good notes.

\(x^2+x^2=PR^2\), so \(2^2+2^2=8\)

From there, we know that \(PR=\sqrt{8}\). That can be simplified to \(2\sqrt{2}\).

Since all angles of triangle PRS = 60, we know that we have an equilateral triangle and all sides are a the same. We're looking for the perimeter of the whole quadrilateral, so side RS and SP will contribute to it. Those are both equal to PR, so we'll take 2 of those, or \(2*2\sqrt{2}\), or more simply, \(4\sqrt{2}\).

We're given that \(x=2\), and 2 of those contribute to the perimeter, so the final perimeter will be \(4+4\sqrt{2}\).

Answer choice B.

Answer must be B as x=2 and triangle QRS is isosceles then 3rd side is 2root 2 so perimeter is sum of all the side 2 sides with 2root 2 and 2 sides with 2 length so total is 4root2+ 4

Since triangle PQR is an isosceles right triangle, side PR = 2√2. Since triangle PRS is an equilateral triangle, PR = RS = PS = 2√2.

So the perimeter of quadrilateral PQRS is 2 + 2 + 2√2 + 2√2 = 4 + 4√2.

Answer: B