Answer

Verified

453.9k+ views

**Hint:**Cuboid – Cuboids are three-dimensional shapes which consist of six faces, eight vertices and twelve edges. Length, width and height of a cuboid are different.

Properties of cuboids.

1. A cuboid is made up of six rectangles, each of the rectangles is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6 faces of cuboid.

2. Base of cuboid – Any face of a cuboid may be called as the base of cuboid.

3. Edges – The edge of the cuboid is a line segment between any two adjacent vertices.

There are 12 edges. AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF and CD

Opposite edges of a cuboid are equal.

4. Vertices – The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid.

A cuboid has 8 vertices

A, B, C, D, E, F, G, H

“All of a cuboid corners (vertices) are 90 degree angles”

5. Diagonal of cuboid – The length of diagonal of the cuboid of given by :

Diagonal of the cuboid $ = \sqrt {({l^2} + {b^2} + {h^2})} $

**Complete step by step solution:**It is given that in cuboid ABCDEFGH.

$HG = 11cm$

$FG = 4cm$

$BF = 8cm$

We have to find AG

In $\Delta EFG,$ angle $EFG = 90^\circ $

Because we know that “all of a cuboids”

And it is given that

$EF = 11cm$ (as opposite sides are equal)

$FG = 4cm$ (given)

So by using Pythagoras theorem we will find EG.

As EG is hypotenuse of triangle EFG so,

$E{G^2} = E{F^2} + F{G^2}$

$E{G^2} = {11^2} + {4^2}$

$E{G^2} = 137$

or

$EG = \sqrt {137} cm$ …..(1)

Now,

In $\Delta AEG,$ angle $AEG = 90^\circ $ (vertex of cuboid)

$AE = 8cm$ (given)

$EG = \sqrt {137} cm$ [from equation (1)]

So we can apply Pythagoras theorem in this triangle.

In $\Delta AEG$

$A{G^2} = A{E^2} + E{G^2}$

$A{G^2} = {8^2} + {(\sqrt {137} )^2}$

$A{G^2} = 64 + 137$

$A{G^2} = 201$

$AG = \sqrt {201} $

or

$AG = 14.17cm$

So, If ABCDEFGH is a cuboid. Then length of $AG = 14.17cm$

**Note:**We can also solve this question by the following method.

We know that in cuboid ABCDEFGH,

AG is the diagonal of cuboid.

So we can directly use the formula for cuboid diagonal.

Diagonal of the cuboid $ = \sqrt {({l^2} + {b^2} + {h^2})} $

Where

$l = length = HG = 11cm$

$b = breadth = FG = 4cm$

$h = height = BF = 8cm$

Substitute these values in above formula,

$AG = \sqrt {({{11}^2} + {4^2} + {8^2})} $

$AG = \sqrt {(121 + 16 + 64)} $

$AG = \sqrt {201} $

$AG = 14.17cm$

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Who was the Governor general of India at the time of class 11 social science CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference Between Plant Cell and Animal Cell