# FIND THE DIAGONAL OF A RECTANGULAR PRISM

Find the length of the diagonal of a rectangular prism :

The following picture shows, how to find the diagonal of a rectangular prism.

Problem 1 :

Find the length of the diagonal D of the following rectangular prism.

Solution :

Considering the base of the rectangular prism, it is in the shape of rectangle.

l = 12 in, w = 5 in

In the base, diagonal length is,

l2 + w2 = d2

122 + 52 = d2

144 + 25 = d2

169 = d2

13 = d

So, the diagonal length of the base is13 in.

Length of the diagonal of the rectangular prism be D.

62 + 132 = D2

36 + 169 = D2

205 = D2

√205 = D

So, the diagonal length of the prism is√205 in.

Problem 2 :

Find the length of the diagonal D of the following rectangular prism.

Solution :

Length = 3 ft, width = 2 ft and height = 10 ft

Diagonal = √32 + 22 + 102

√9+4+100

√113 inches

Problem 3 :

Find the length of the diagonal D of the following rectangular prism.

Solution :

Length = 7 ft, width = 3 ft and height = 4 ft

Diagonal = √72 + 32 + 42

√49 + 9 + 16

√74 ft

Problem 4 :

Find the length of the diagonal D of the following rectangular prism.

Solution :

Length = 10 ft, width = 6 ft and height = 15 ft

Diagonal = √102 + 62 + 152

√100 + 36 + 225

√361

= 19 ft

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