Height of the cuboid

Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?

Correct answer:

c =  12 cm

Step-by-step explanation:

$$\begin{gathered} a=3\text{ cm } \\ b=4\text{ cm } \\ u=13\text{ cm } \\ {s}^2=a^2+b^2 \\ s=\sqrt{a^2+b^2}=\sqrt{3^2+4^2}=5\text{ cm } \\ {u}^2=c^2+s^2 \\ c=\sqrt{u^2-s^2}=\sqrt{13^2-5^2}=12\text{ cm} \end{gathered}$$

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