n the figure below, PQRS is a parallelogram of perimeter 26 and area 28. What is the perimeter of rectangle QOST?
+1641 perimeter is 28 sides of triangle STR are 3-4-5 PS = 28 / ST = 7
+129899 Since SR = 5 then so is QP
And since the perimeter of PQRS is 26, then QR = (26 - 10) / 2 = 16/2 = 8
And the area of PQRS = QR * ST
So
28 = 8 * ST
28/8 = ST
7/2 = ST = 3.5
And using the Pythagorean Theorem
RT^2 + ST^2 = RS^2
RT^2 + (3.5)^2 = 5^2
RT^2 = 5^2 - 3.5^2
RT^2 = 25 - 12.25
RT^2 = 12.75
RT = sqrt (12.75)
Perimeter of QOST = 2 ( QR + RT + ST) = 2 ( 8 + sqrt (12.75) + 3.75) =
23 + 2sqrt (12.75)
and the first answer is incorrect too!!!
