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telo118 [61]
3 years ago
14

What are the values the values of a and b?

Mathematics
1 answer:
Setler [38]3 years ago
4 0
The segment marked 20 is the geometric mean of the two pieces into which it splits the hypotenuse. You get the proportion

\frac{20}{a} = \frac{21}{20}

Solving,

21a =(20)(20) \\ 21a = 400 \\ a = \frac{400}{21}

To find  b,  use the fact that  b  is the geometric mean of the whole hypotenuse, 21 + a, and the part that is attached to it,  a.

\frac{b}{a} = \frac{21+a}{b}

A little arithmetic shows that 21+a = \frac{841}{21}.

\frac{b}{\frac{400}{21}} = \frac{\frac{841}{21}}{b} \\ b^2 = \frac{336400}{441} \\ b=\frac{580}{21}
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