Connect with a global community of experts on IDNLearn.com. Ask anything and receive comprehensive, well-informed responses from our dedicated team of experts.

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 :

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

#SPJ2

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.