Answer:
The height of her friend is 4.826 feet.
Step-by-step explanation:
The length of the shadow ([tex]x_{S}[/tex]), measured in feet, is directly proportional to the height of the person ([tex]x_{P}[/tex]), measured in feet. That is:
[tex]x_{P} \propto x_{S}[/tex]
[tex]x_{P} = k\cdot x_{S}[/tex] (1)
Where [tex]k[/tex] is the proportionality constant, no unit.
We can eliminate this constant by constructing this relationship:
[tex]\frac{x_{P,M}}{x_{S,M}} = \frac{x_{P,F}}{x_{S,F}}[/tex] (2)
Where M and F represents Melody and Melody's friend. If we know that [tex]x_{P,M} = 5\,ft[/tex], [tex]x_{S,M} = 7\,ft[/tex] and [tex]x_{S,F} = 6\,ft[/tex], then the height of his friend is:
[tex]x_{P,F} = \left(\frac{x_{P,M}}{x_{S,M}} \right)\cdot x_{S,F}[/tex]
[tex]x_{P,F} = \left(\frac{5\,ft}{7\,ft}\right)\cdot (6\,ft)[/tex]
[tex]x_{P,F} = 4.286\,ft[/tex]
The height of her friend is 4.826 feet.
