Cuboid - volume, diagonals

The length of the one base edge of cuboid a is 3 cm. The body diagonal is ut=13 cm, and the diagonal of the cuboid's base is u1=5 cm. What is the volume of the cuboid?

Correct answer:

V =  144 cm³

Step-by-step explanation:

$$\begin{gathered} a=3\text{cm} \\ {u}_1=5\text{cm} \\ b=\sqrt{u_1^2-a^2}=\sqrt{5^2-3^2}=4\text{cm} \\ c=\sqrt{13^2-u_1^2}=\sqrt{13^2-5^2}=12\text{cm} \\ V=a\cdot b\cdot c=3\cdot 4\cdot 12=144{\text{cm}}^3 \end{gathered}$$

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