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Let P be the point (0,5), let Q be the point (6,9), and let R be the point (12,0). Determine the area of right-angled triangle PQR.

 Sep 11, 2018
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Let  PQ  be one leg and QR  be the other leg

 

PQ  = sqrt  [ 6^2 + ( 9- 5)^2 ] =   sqrt [ 36  + 4^2 ] = sqrt [52]

 

QR  = sqrt [ (12 - 6)^2  + 9^2  ]  =  sqrt  [ 6^2 + 9^2 ] =  sqrt [ 117]

 

And the area of a right triangle  = (1/2) (product of the leg lengths)  =

 

(1/2)sqrt(52)sqrt(117)  = (1/2) sqrt(6084)  = (1/2) 78   =   39 units^2

 

 

 

cool cool cool

 Sep 11, 2018

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