Question

Find the diagonal of the rectangular solid with the given measures. l = 18, w = 10, h = 2

Answer 1

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 :

`(Hypotenuse)^2=(Perpendicular)^2+(Base)^2`

`(AC)^2=(AB)^2+(BC)^2`

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.

`(AC)^2=(18)^2+(10)^2`

`AC=√((18)^2+(10)^2)`

`AC=√(324+100)`

`AC=√(424)`

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

Using Pythagoras theorem in ΔACD :

`(Hypotenuse)^2=(Perpendicular)^2+(Base)^2`

`(AD)^2=(AC)^2+(CD)^2`

Given:

Side AC =
`√(424)`

Side CD = h = 2

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

`(AD)^2=(√(424))^2+(2)^2`

`AD=\sqrt{(√(424))^2+(2)^2}`

`AD=√(424+4)`

`AD=√(428)`

`AD=20.69`

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

Answer 2

`\boxed{d=2√(107)}`

Explanation:

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

`d=\sqrt{a^(2)+b^(2)+c^(2)}`

So here, we know that:

`a=l=18 \\ \\ b=w=10 \\ \\ c=h=2`

So:

`d=\sqrt{l^(2)+w^(2)+h^(2)} \\ \\ d=\sqrt{18^(2)+10^(2)+2^(2)} \\ \\ d=√(324+100+4) \\ \\ d=√(428) \\ \\ \boxed{d=2√(107)}`