in the figure below, PQRS is a parallelogram of perimeter 24 
and area of 28 What is the perimeter of rectangle QOST? Include an explanation of how you solved the problem
+128408 Since SR parallel to PQ....they are equal
So....to find PS = QR we have
24 - 2SR = PS + QR
24 -2(5) = PS + QR
24 - 10 = PS + QR
14 = PS + QR
So QR = 7 = PS
And the area of the parallelogram PQRS = QR * ST
So
28 = 7 * ST divide both sides by 7
4 = ST = OQ
And using the Pythagorean Theorem
RT = sqrt [ RS^2 - ST^2] = sqrt [ 5^2 - 4^2] = sqrt [ 25 - 16] = sqrt[9] = 3 = OP
So....the perimeter of QOST =
2 (OP + PS) + 2(ST) =
2 (3 + 7) + 2(4) =
2*10 + 2*4 =
28 units
