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Each leg of the right triangle has length 6 cm.  Find the area of the green square.

 

 Dec 27, 2020
 #1
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+1

Dividing this into 9 segments, we find that the square takes up 4 segments. 4/9 * the area of the triangle = 4/9*18=
 

8

 Dec 27, 2020
 #2
avatar+859 
+4

Square side is a

 

2(a / tan45º) + a = √72           a = √8           A = 8 cm2

 Dec 27, 2020
edited by jugoslav  Dec 27, 2020
 #3
avatar+114325 
+1

Let A  =  (0,6)   B  = (0,0)   and C = (6,0)

 

 

 

AC   =    6sqrt (2)

 

Triangle   ADE  is similar to  triangle ABC

Call the  side of the square, S =  DE

So

AD/ DE  = AB/BC

AD /S  = 6/6

AD  = S

 

And triangle   CFG is similar to triangle CBA

So

FG/ CF  = BA/ CB

S / CF  = 6/6

CF = S

 

So

 

AD + DF  + FC   =  6sqrt (2)

 

S  + S + S    = 6sqrt (2)

 

3S  = 6sqrt (2)

 

S  = 2sqrt (2)  =  sqrt(8)  cm

 

Area of square  = 8  cm^2

 

 

cool cool cool

 Dec 27, 2020

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