In the figure below, PQRS is a parallelogram of perimeter 24 and area 28. What is the perimeter of rectangle QOST? Include an explanation of how you solved the problem.

https://ibb.co/cRERSS

sageatron2000
Apr 18, 2018

#1**+1 **

Sincs RS = 5.....then PQ also equals 5 since RS is parallel to PQ

So using the perimeter.... PS + QR = 24 - 5 - 5 = 14

And since PS = QR then

2OR = 14 divide both sides by 2

QR = 7

And the area of PQRS = ( Base * Height) = (QR * Height)

So

28 = 7 * Height divide both sides by 7

4 = Height = ST

And by the Pythagorean Theorem

RT = sqrt [ RS^2 - ST^2] = sqrt [ 5^2 - 4^2] = sqrt [ 25 - 16 ] = sqrt (9) = 3

So....the base of QOST = QT = QR + RT = 7 + 3 = 10

So the area of QOST =

QT * ST =

10 * 4 =

40 units^2

CPhill
Apr 18, 2018

#2**+1 **

Since the perimeter of PQRS = 24 and QP=RS = 5 + 5 = 10. Therefore PS=QR =[24 - 10] / 2 = 7

And since the area of PQRS = 28, therefore the Height =28/7 **=4=ST**, since area of PQRS = base x height.Therefore the right triangle RST is a 3, 4, 5 triangle with RT = 3.

RT + QR =3 + 7 **=10 =QT**. **Therefore the perimeter of the rectangle QOST =2[4 +10] = 28.**

**CPhill: I think the young person wants the PERIMETER, not the Area.**

Guest Apr 18, 2018

edited by
Guest
Apr 18, 2018