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In a certain isosceles right triangle, the altitude to the hypotenuse has length 6. What is the hypotenuse of the triangle?

 Mar 30, 2021
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We  have  the following relationship

 

(1/2) length of hypotenuse  / 6   =  6  /  (1/2) length of hypotenuse

 

cross - multiply

 

[ (1/2)lengt of hypotenuse ] ^2  =  6 * 6

 

[ (1/2) length of hypotenuse ] ^2   =  36          take  the postive root of both sides

 

(1/2) length of hypotenuse  =  6

 

So

 

Length of hypotenuse  =  2 * 6   =  12

 

cool cool cool

 Mar 30, 2021

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