Respuesta :

danielmaduroh

Answer:

[tex]\boxed{d=2\sqrt{107}}[/tex]

Step-by-step explanation:

For a rectangular prism whose side lengths are [tex]a,\:b\:and\:c[/tex] the internal diagonal can be calculated as:

[tex]d=\sqrt{a^{2}+b^{2}+c^{2}}[/tex]

So here, we know that:

[tex]a=l=18 \\ \\ b=w=10 \\ \\ c=h=2[/tex]

So:

[tex]d=\sqrt{l^{2}+w^{2}+h^{2}} \\ \\ d=\sqrt{18^{2}+10^{2}+2^{2}} \\ \\ d=\sqrt{324+100+4} \\ \\ d=\sqrt{428} \\ \\ \boxed{d=2\sqrt{107}}[/tex]

Answer : The value of diagonal of the rectangular solid is, 20.69 unit.

Step-by-step explanation :

First we have to calculate the side AC.

Using Pythagoras theorem in ΔABC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

Given:

Side AB = l = 18

Side BC = w =  10

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(18)^2+(10)^2[/tex]

[tex]AC=\sqrt{(18)^2+(10)^2}[/tex]

[tex]AC=\sqrt{324+100}[/tex]

[tex]AC=\sqrt{424}[/tex]

Now we have to calculate the side AD (diagonal).

Using Pythagoras theorem in ΔACD :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](AD)^2=(AC)^2+(CD)^2[/tex]

Given:

Side AC = [tex]\sqrt{424}[/tex]

Side CD = h =  2

Now put all the values in the above expression, we get the value of side AD.

[tex](AD)^2=(\sqrt{424})^2+(2)^2[/tex]

[tex]AD=\sqrt{(\sqrt{424})^2+(2)^2}[/tex]

[tex]AD=\sqrt{424+4}[/tex]

[tex]AD=\sqrt{428}[/tex]

[tex]AD=20.69[/tex]

Thus, the value of diagonal of the rectangular solid is, 20.69 unit.

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