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# help

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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.

SmartMathMan  Dec 7, 2017
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If the permeter of PQRS  is 24....remember that PQ  = SR   and   PS  = QR

So...... PQ  + SR  +  PS + QR  = 24

5  +  5    + PS + QR   =   24       sub  PS for QR

10  +  PS  + PS  =  24       subtract 10 on each side

2PS  =   14     divide both sides by 2

PS  = 7  = QR

And the area of PQRS   =  PS  * height of PQRS (=ST)  ......so we have that

28  = 7 * ST    divide both sides by 7

4  = ST

And since RST is a right triangle.... using the Pythagorean Theorem...

RS^2 - ST^2  =  RT^2

5^2  - 4^2  = RT^2

25  - 16  = RT^2

9  = RT^2      take the square root of both sides

3  = RT

So........QT  = QR + RT  =    PS + RT  =    7 + 3   = 10

So...the perimeter of  QOST  =  2 [ QT + ST]  = 2 [ 10 +  4]  =  2 * 14  =  28

CPhill  Dec 7, 2017
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thx so much man

SmartMathMan  Dec 7, 2017

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