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Yuki888 [10]
3 years ago
12

usa el teorema de la altura para proponer como se podria construir un segmento cuya longitud sea media proporcional entre dos se

gmentos de 4 cm y 9 cm.¿como se podria construir si los segmentos son de a cm y b cm?

Mathematics
1 answer:
Mrac [35]3 years ago
6 0
Usando el teorema de altura 

El teorema de altura relaciona la altura (h) de un triángulo rectángulo (ver figura) y los catetos de dos triángulos que son semejantes al anterior ABC, al trazar la altura (h) sobre la hipotenusa. De manera que e<span>n todo </span>triángulo rectángulo, la altura (h<span>) relativa a la </span>hipotenusa<span> es la </span>media geométrica<span> de las dos proyecciones de los </span>catetos<span> sobre la </span>hipotenusa<span> (</span>n<span> y </span>m<span>). Es decir, se cumple que:

</span>\frac{n}{h}= \frac{h}{m}

Dado que el problema establece <span>construir un segmento cuya longitud sea media proporcional entre dos segmentos de 4 y 9 cm, entonces, digamos que n = 4cm y m = 9cm tenmos que:

</span>\frac{4}{h}= \frac{h}{9}

De donde:

h= \sqrt{(4)(9)}=\sqrt{36}=6cm

¿Cómo se podria construir si los segmentos son de a cm y b cm?

Si los segmentos son de a y b cm entonces a y b son parámetros que pueden tomar cualquier valor positivo siempre que se cumpla que:

h= \sqrt{ab}

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