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The above diagram shows two right triangles 6-8-10 and 8-15-17 joined to form a large triangle with side lengths 10-17-21.

What is the area of this large triangle?

 

 Jan 8, 2020
 #1
avatar+107099 
+1

By the Pythagorean Theorem the height of the large triangle  is given by

 

sqrt  [ 10^2 - 6^2 ]   = sqrt  [100 - 36 ]  =  sqrt (64)   =8

 

So  the  area  of the large triangle  is given by

 

(1/2) (base) (height)  =

 

(1/2) ( 6+15) (8)  =

 

(1/2) (21) (8)  =

 

4 * 21  =

 

84 units^2

 

cool cool cool

 Jan 8, 2020
 #2
avatar+333 
+1

You can solve this one in your head in less then a minute.

                    A = 4*6 + 4*15    wink

 Jan 8, 2020

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