Calcula la suma de las longitudes de los catetos, si la hipotenusa mide 15 u y la altura relativa a ella mide 6 u. UwU

9 sqrt(5)

Step-by-step explanation:

La altura relativa a la hipotenusa corta la hipotenusa en dos segmentos.

Defina x como

x = la longitud de uno de esos segmentos

Entonces, la longitud del otro segmento = 15 - x.

Entonces, por el teorema, tenemos que (15-x) (x) = 36, de modo que

15x - x ^ 2 = 36

x ^ 2 - 15x + 36 = 0

(x-3) (x-12) = 0

Entonces, x = 3 o x = 12.

Sin pérdida de generalidad. sea x = 3.

Entonces, la suma de las dos piernas es

raíz cuadrada (6 ^ 2 + 3 ^ 2) + raíz cuadrada (12 ^ 2 + 6 ^ 2) =

raíz cuadrada (36 + 9) + raíz cuadrada (144 + 36) =

raíz cuadrada (45) + raíz cuadrada (180) =

raíz cuadrada (9 * 5) + raíz cuadrada (36 * 5) =

3 raíz cuadrada (5) + 6 raíz cuadrada (5) =

9 cuadrados (5)

17.08

correct me if i am wrong.

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