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In right triangle ABC, AC = 8, AB = 15, and BC = 17. Square ADEF is inscribed in the square. Find the side length of square ADEF.

 

 Dec 6, 2021
 #1
avatar+22572 
+1

Triangle(CDE)  is similar to  triangle(CAB).

 

Therefore:  CD / DE  =  CA / AB

 

Since  AD = x   --->   DE = x.

 

Since  CA = 8  and  AD = x   --->   CD = 8 - x.

 

Substituting:  CD / DE  =  CA / AB     --->     (8 - x) / x  =  8 / 15

 

Cross-multiplying:  8x  =  120 - 15x     --->   x  =  5.217

 Dec 6, 2021
 #2
avatar+1622 
+2

15/8(8 - x) = 8/15(15 - x)

 

x = 120/23

 Dec 7, 2021

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