Answer:
w=5 cm
Step-by-step explanation:
Functions
We know the height (h) of a box is a function of the width of its base:
[tex]\displaystyle h=\frac{500}{w^2}[/tex]
We are required to find the width of the box when the height is h=20 cm
To find w in terms of h we must isolate w from the equation above
Operating
[tex]\displaystyle w^2h=500[/tex]
[tex]\displaystyle w^2=\frac{500}{h}[/tex]
Taking the square root
[tex]\displaystyle w= \sqrt{\frac{500}{h}}[/tex]
Replacing the value of h=20
[tex]\displaystyle w= \sqrt{\frac{500}{20}}= \sqrt{25}=\ 5cm[/tex]
[tex]\boxed{w=5\ cm}[/tex]
