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Right triangle ABC has side lenghts AB = 3, BC = 5. Square XYZW is inscribed in triangle ABC with X and Y on line AB, and Z on line BC. What is the side length of the square.

 

 
 Jul 20, 2021
 #1
avatar+733 
+2

$\triangle ZYC \sim \triangle WBZ \sim \triangle ABC$

Let the length of the square be $s.$

$\frac{CZ}{s} = \frac{5}{3} \Rightarrow CZ = \frac{5}{3} s$

$\frac{ZB}{s} = \frac{4}{5} \Rightarrow ZB = \frac{4}{5}s$

$\frac{5}{3} s + \frac{4}{5}s = CZ + ZB = 4.$

$25s +12s = 60$

$37s = 60$

$s=\frac{60}{37}$

 
 Jul 20, 2021
 #2
avatar+1439 
+2

Neat job, MPS!!! smiley

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5a/3 + a + 3a/5 = √34

 

 
civonamzuk  Jul 20, 2021
edited by civonamzuk  Jul 21, 2021
edited by civonamzuk  Jul 21, 2021

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