Each dimension of a larger rectangular field is 4.5 times greater than a smaller rectangular field. If it costs $176 to seed the smaller field, how much would it cost to seed the larger field with the same type of seeds?

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13-06-2017
Mathematics

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Each dimension of a larger rectangular field is 4.5 times greater than a smaller rectangular field. If it costs $176 to seed the smaller field, how much would it cost to seed the larger field with the same type of seeds?

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jdoe0001 jdoe0001 · Answer 1 · 2017-06-13T20:51:56+02:00

[tex]\bf \textit{area of a rectangle}\\\\ A=\boxed{lw}\qquad \begin{cases} l=length\\ w=width\\ -----\\ l=4.5l\\ w=4.5w \end{cases}\implies A=4.5l\cdot 4.5w \\\\\\ A=4.5^2lw\implies A=20.25\boxed{lw}[/tex]

so... if the length and width get increased by 4.5, how much does the area increase by?

well, for the smaller field, the area is just "lw", once you got to the larger field, and the length and width are 4.5 larger, then the area becomes 20.25 larger

now, if it costs to $176 to seed "lw", 176=lw, it'll cost 20.25*lw, or 20.25*176 to seed the larger 4.5 field