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What is the length of the diagonal, d, of the rectangular prism shown below?
Round your answer to the nearest tenth.

What Is The Length Of The Diagonal D Of The Rectangular Prism Shown Below Round Your Answer To The Nearest Tenth class=

Sagot :

gvimalaratnam21

Answer:

d = 9.6 (1dp)

Step-by-step explanation:

Based on the picture below

Using Pythagoras

[tex]a^{2} + b^{2} = c^{2} \\8^{2} + 2^{2} = x^{2} \\64 + 4 = x^{2} \\68 = x^{2} \\x = \sqrt{68}\\[/tex]

Using Pythagoras

[tex]a^{2} + b^{2} = c^{2} \\5^{2} + (\sqrt{68})^{2} = d^{2}\\25 + 68 = d^{2}\\93 = d^{2}\\d = \sqrt{93}\\d = 9.64365...\\d = 9.6 (1dp)[/tex]

View image gvimalaratnam21

The length of the diagonal, d, of the rectangular prism is  9.6  .

What is rectangular prism?

A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

What is the length of diagonal of rectangular prism ?

The formula for the length of the diagonal of a right rectangular prism is :

[tex]\sqrt{l^{2} +b^{2} +h^{2} }[/tex]

where l is the length, b is the breadth and h is the height of a right rectangular prism.

According to the question

Length of rectangular prism  = 5

Breath of rectangular prism  = 8

Height of rectangular prism  = 2

Now,

The diagonal of rectangular prism =  d

By using the formula of  the length of the diagonal of a  rectangular prism is :

[tex]\sqrt{l^{2} +b^{2} +h^{2} }[/tex]

Substituting the value in formula

[tex]\sqrt{l^{2} +b^{2} +h^{2} }[/tex]  = d

[tex]\sqrt{5^{2} +8^{2} +2^{2} }[/tex]  = d

[tex]\sqrt{25 +64 +4 }[/tex]  = d

[tex]\sqrt{93 }[/tex]  = d

Therefore,

d = 9.6  

Hence, the length of the diagonal, d, of the rectangular prism is  9.6  .

To know more about rectangular prism and its diagonal  here:

https://brainly.com/question/12517010

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