Base side

In a quadrilateral prism, are known surface area S = 12400 mm², base side m = 40mm, and prism height = 120mm. What is the length of base side n =?

Correct answer:

n =  8.75 mm

Step-by-step explanation:

$$\begin{gathered} S=12400{\text{mm}}^2 \\ m=40\text{mm} \\ h=120\text{mm} \\ {S}_1=m^2=40^2=1600{\text{mm}}^2 \\ S=2\cdot (m\cdot n+n\cdot h+h\cdot m) \\ 12400=2\cdot (40\cdot n+n\cdot 120+120\cdot 40) \\ 320n=2800 \\ n=\frac{2800}{320}=8.75=8.75\text{mm} \\ n=\frac{35}{4}=8.75 \\ \text{ Verifying Solution: } \\ A=2\cdot (m\cdot n+n\cdot h+h\cdot m)=2\cdot (40\cdot 8.75+8.75\cdot 120+120\cdot 40)=12400{\text{mm}}^2 \end{gathered}$$

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