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Use the figure below to solve for the value of x.

Use the figure below to solve for the value of x.-example-1
User Zheng Qu
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1 Answer

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Given:

A figure of a right triangle and an altitude form the right angle vertex to hypotenuse.

To find:

The value of x.

Solution:

From the given figure, it is clear that the altitude divides the hypotenuse in two segments x and 8.

Length of altitude = 18

If an altitude divide the hypotenuse in 2 segments, then according to the geometric mean theorem, the length of the altitude is the geometric mean of two segments of hypotenuse.

By using geometric mean theorem, we get


18=√(x* 8)
[\because \text{Geometric mean of }a,b,c:b=√(ac)]


18^2=8x


324=8x

Divide both sides by 8.


(324)/(8)=x


40.5=x

Therefore, the value of x is 40.5.

User Fastobject
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