Question #349431

In a rectangular parallelepiped, the length and the width of the base are 12 in. and 9

in., respectively. Find the volume if the length of the diagonal of the solid is 25 inches.


1
Expert's answer
2022-06-10T10:47:21-0400

Given a=12 in,b=9 in,a2+b2+c2=25 in.a=12\ in, b=9 \ in, \sqrt{a^2+b^2+c^2}=25\ in.

Substitute


122+92+c2=25212^2+9^2+c^2=25^2

c2=400,c>0c^2=400, c>0

c=20 inc=20\ in

V=abc=12(9)(20)=2160(in3)V=abc=12(9)(20)=2160({in}^3)

2160 cubic inches



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