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

Guest Dec 3, 2018

#1**+1 **

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

CPhill Dec 3, 2018