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Problem 829

In the rectangular solid shown, \(\underline{D A}=4\) in. \(\underline{D C}=3\), and \(\underline{\mathrm{GC}}=12\). (a) Find the length of \(\underline{\mathrm{CA}}\), a diagonal of the base \(\mathrm{ABCD}\). (b) Using the result found in part (a), find the length of \(\underline{G A}\). a diagonal of the solid. (c) If \(\underline{\mathrm{DA}}=\ell, \underline{\mathrm{DC}}=\mathrm{w}\), and \(\underline{\mathrm{GC}}=\mathrm{h}\), represent the length of

Expert verified

In summary, we found:
(a) The length of the diagonal of the base, \(\underline{\mathrm{CA}} = 5\).
(b) The length of the diagonal of the solid, \(\underline{G A} = 13\).
(c) The length of the diagonal of the solid, \(\underline{G A}\), can be represented in terms of \(\ell, \mathrm{w}\), and \(\mathrm{h}\) as: \(\underline{G A} = \sqrt{h^2 + \ell^2 + w^2}\).

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