n the figure below, PQRS is a parallelogram of perimeter 26 and area 28. What is the perimeter of rectangle QOST?

Guest Nov 17, 2020

#1**-1 **

perimeter is 28 sides of triangle STR are 3-4-5 PS = 28 / ST = 7

jugoslav Nov 17, 2020

edited by
Guest
Nov 17, 2020

#2**+2 **

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)

CPhill Nov 17, 2020