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An isosceles right triangle is removed from each corner of a square piece of paper, as shown, to create a rectangle. If \(AB=12\) units, what is the combined area of the four removed triangles, in square units?

 Jul 6, 2022
 #1
avatar
-1

The combined area of the four removed triangles is 60.

 Jul 6, 2022
 #2
avatar+1155 
+7

What's your explanation?

nerdiest  Jul 6, 2022
 #3
avatar+1155 
+7

image not shown.

 

 

look below

nerdiest  Jul 6, 2022
edited by nerdiest  Jul 6, 2022
 #4
avatar+124676 
+1

Nothing shown......

 

 

cool cool cool

 Jul 6, 2022
 #6
avatar+1155 
+8

here. SORRY. no words to explain. how dumb. i am.

nerdiest  Jul 6, 2022
edited by nerdiest  Jul 6, 2022
 #5
avatar
+2

 

An isosceles right triangle is removed from each corner of a square piece of paper, as shown, to create a rectangle.  

 

"as shown" huh?  There's nothing shown. 

 

As long as this is a guessing game, my submission is either 36 or 144.  Pick one.    

 Jul 6, 2022
 #7
avatar+1155 
+8

my bad. you can downvote me. no words to explain. how dumb. i am.

nerdiest  Jul 6, 2022
 #13
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+2

 

nerdi, since I'm posting as a guest, I'm not allowed to vote.  I wouldn't down vote you anyway. 

.

Guest Jul 7, 2022
 #14
avatar+1155 
+8

thx and sorry 

nerdiest  Jul 7, 2022
 #8
avatar+124676 
+2

Call the equal sides of  the  small isosceles triangle  ,  a

Call the equal sides of the larger isosceles triangle, b

 

The short side of the  rectangle in the middle =  sqrt (a^2 + a^2)  =  sqrt (2a^2) = a sqrt (2)

 

The long side of  the rectangle in the  middle = sqrt (b^2 + b^2)  =sqrt (2b^2)  = b sqrt (2)

 

By the Pythagorem Theorem

 

[ asqrt (2)]^2  +   [b sqrt (2) ]^2  = AB^2

 

[a sqrt (2) ] ^2  + [ b sqrt (2) ] ^2  = 12^2

 

2a^2 + 2b^2  =  144    divide by 2

 

a^2 + b^2  = 72

 

But a^2 = the area of the two smaller isosceles triangles

And b^2 = the area of the larger two isosceles triangles

 

So....their combined area =    72

 

 

cool cool cool

 Jul 6, 2022
edited by CPhill  Jul 6, 2022
edited by CPhill  Jul 6, 2022
 #9
avatar+1155 
+9

.......

no words to explain how genius you are.

nerdiest  Jul 6, 2022
 #10
avatar+124676 
+3

LOL!!!

 

Thx....I just get lucky once in a while  !!!!!

 

 

cool cool cool

CPhill  Jul 6, 2022
 #11
avatar+2448 
0

That's a really neat solution, Chris!

BuilderBoi  Jul 6, 2022
 #12
avatar+124676 
+3

Thx, BuilderBoi  !!!!!

 

 

cool cool cool

CPhill  Jul 6, 2022

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