Length = 3 width

The length of a cuboid is thrice its width. The height and volume of the cuboid measure 4cm and 300 cubic cm, respectively. What is the length of this cuboid?

Correct answer:

l =  15 cm
w =  5 cm

Step-by-step explanation:

$$\begin{gathered} l=3w \\ h=4\text{cm} \\ V=300{\text{cm}}^3 \\ V=lwh \\ V=3wwh=3w^{2}h \\ w=\sqrt{\frac{V}{3\cdot h}}=\sqrt{\frac{300}{3\cdot 4}}=5\text{cm} \\ l=3\cdot w=3\cdot 5=15\text{cm} \end{gathered}$$

$$\begin{gathered} w=5=5\text{cm} \\ \text{ Verifying Solution: } \\ {V}_2=l\cdot w\cdot h=15\cdot 5\cdot 4=300{\text{cm}}^3 \end{gathered}$$

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