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Sagot :
We have a rectangular box where we know the area of the faces and we have to find the width w, length l and height h.
The area of the top of the box is equal to the length times the width (l*w) and we also know that it is 42 cm², so we can write:
[tex]l\cdot w=42[/tex]With the same logic, we can write the equations for the other two areas:
[tex]\begin{gathered} l\cdot h=30 \\ w\cdot h=35 \end{gathered}[/tex]NOTE: the area we choose for l or w is indistinct,so we can relate it as we like.
Then, we can solve this system of equations substituting variables as:
[tex]\begin{gathered} l\cdot h=30\longrightarrow l=\frac{30}{h} \\ w\cdot h=35\longrightarrow w=\frac{35}{h} \\ l\cdot w=(\frac{30}{h})(\frac{35}{h})=\frac{1050}{h^2}=42 \\ h^2=\frac{1050}{42} \\ h^2=25 \\ h=\sqrt[]{25} \\ h=5 \end{gathered}[/tex]With the value of h, we can calculate l and w:
[tex]\begin{gathered} l=\frac{30}{h}=\frac{30}{5}=6 \\ w=\frac{35}{h}=\frac{35}{5}=7 \end{gathered}[/tex]Answer:
The dimensions of the box are: length = 6 cm, width = 7 cm and height = 5 cm.
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