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In a certain isosceles right triangle, the altitude to the hypotenuse has length 8. What is the area of the triangle?

 Mar 30, 2021
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We  have  the following relationship

 

(1/2) hypotenuse length  / 8   =  8 / ( 1/2) hypotenuse length

 

cross-multiply

 

[(1/2) hypoenuse  length] ^2  = 8 * 8

 

 [(1/2) hypotenuse ]^2  =  64         take  the  sqrt  of both sides

 

(1/2) hypotenuse length  =  8

 

Area  =  (1/2) hypotenuse length * altitude =   8 * 8  =   64

 

cool cool cool

 Mar 30, 2021

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