Find the exact value of y.

Wribreeminsl

Wribreeminsl

Answered question

2020-11-24

Find the exact value of y.

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2020-11-25Added 104 answers

According to the Geometric Mean Theorem, if a right triangle's altitude, x, splits the hypotenuse into two segments with lengths of a and b, then x2=ab. 
As seen in the picture, the hypotenuse is split into segments with lengths of 5 and 8 by the altitude, which is denoted by y. By the Geometric Mean Theorem, we then have y2=5⋅8. 
Multiplying 5 and 8 gives y2=40. 
Square rooting both sides gives y=40. 
Simplifying the root then gives y=40=(410)=410=210. 
Therefore y=210.

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