Question

ayuda es para hoy Calcula la medida de la diagonal del prisma. *

Answer 1

Respuesta:

          [tex]25cm[/tex]

Explicación paso a paso:

[tex]Largo: L[/tex]

[tex]Ancho: a[/tex]

[tex]Alto: h = 15cm[/tex]

Diagonal de la cara de la base:  [tex]d = 20cm[/tex]

Diagonal del prisma: D = ?

Por Pitágoras:

[tex]a^{2} +L^{2} = d^{2}[/tex]

[tex]a^{2} +L^{2} = 20^{2}[/tex]

[tex]a^{2} +L^{2} = 400[/tex]    [tex]ecuac.1[/tex]

[tex]a^{2} +L^{2} +h^{2} = D^{2}[/tex]

[tex]a^{2} +L^{2} + 15^{2} = D^{2}[/tex]     [tex]ecuac.2[/tex]

Restando ecuac.2   y  ecuac.1

[tex]a^{2} +L^{2} +15^{2} = D^{2}[/tex]

[tex]-a^{2} -L^{2} = -400[/tex]

________________

                [tex]+15^{2} = D^{2} -400[/tex]

[tex]+225 +400 = D^{2}[/tex]

 [tex]625 = D^{2}[/tex]

[tex]D = \sqrt{625}[/tex]

[tex]D = 25 cm[/tex]

La medida de la diagonal del prisma es:   [tex]25cm[/tex]