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A square is inscribed in a right triangle. The legs of the triangle are 2 and 3. Find the side length of the square.

 May 13, 2020
 #1
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We can use similar triangles to solve this....see the following image

 

 

Let AD  be  one side of the square

And let   DE  be the  other side of the square

 

And  using  similar riangles, we  have  that triangle  BDE is similar to triangle BAC

 

So

 

BD/ DE  =  BA/ AC

 

BD/ DE =  2 / 3

 

But DE = AD

 

So

 

BD / AD   =  2/3

 

BD : AD  = 2 : 3

 

So there are 5 equal parts of AB  and AD is 3 of them...so AD = (3/5)(AB)  = (3/5)(2) = 6/5  = side of the square

 

 

 

 

cool cool cool 

 May 13, 2020

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