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A parallelogram has sides measuring 7 and 9. Its shorter diagonal has a length of 8.  Find the measure of the longer diagonal.

 Jun 12, 2021
 #1
avatar+121056 
+2

Parallelogram Law :  The  sum of  the squares  of the four sides of a parallelogram  = the  sum of the squares of the diagonals

 

So

 

2*7^2   + 2*9^2  =  8^2  +  x^2

 

98  + 162  =  64 + x^2

 

98  + 162  - 64   = x^2

 

196  = x^2

 

sqrt (196)  = x   = 14  =  the longer diagonal

 

 

cool cool cool

 Jun 12, 2021
edited by CPhill  Jun 12, 2021
 #2
avatar+34326 
0

THAT is a really obscure law I did  NOT know about !!   cheeky

ElectricPavlov  Jun 12, 2021
 #3
avatar+121056 
0

See here, EP  :

 

https://en.wikipedia.org/wiki/Parallelogram_law

 

 

cool cool cool

CPhill  Jun 12, 2021
 #4
avatar+34326 
0

Good to know in my everyday life .....  haha        Thanx !   ~ EP

ElectricPavlov  Jun 12, 2021
 #5
avatar+121056 
0

LOL!!!!

 

 

cool cool cool

CPhill  Jun 12, 2021

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