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,
l^{2} + w^{2} = d^{2}
12^{2} + 5^{2} = d^{2}
144 + 25 = d^{2}
169 = d^{2}
13 = d
So, the diagonal length of the base is13 in.
Length of the diagonal of the rectangular prism be D.
6^{2} + 13^{2} = D^{2}
36 + 169 = D^{2}
205 = D^{2}
√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 = √3^{2} + 2^{2} + 10^{2}
= √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 = √7^{2} + 3^{2} + 4^{2}
= √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 = √10^{2} + 6^{2} + 15^{2}
= √100 + 36 + 225
= √361
= 19 ft
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