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Given:
A rectangular piece of land has an area of [tex]\dfrac{3}{4}[/tex] square mile.
The land is [tex]2\dfrac{1}{2}[/tex] miles long.
To find:
The width of the rectangular land.
Solution:
We have,
Area of a rectangle = [tex]\dfrac{3}{4}[/tex] square mile.
Length = [tex]2\dfrac{1}{2}[/tex] miles
We know that, area of a rectangle is
[tex]A=l\times b[/tex]
[tex]\dfrac{3}{4}=2\dfrac{1}{2}\times b[/tex]
[tex]\dfrac{3}{4}=\dfrac{2(2)+1}{2}b[/tex]
[tex]\dfrac{3}{4}=\dfrac{5}{2}b[/tex]
Multiply both sides by [tex]\dfrac{2}{5}[/tex], we get
[tex]\dfrac{2}{5}\times \dfrac{3}{4}=\dfrac{2}{5}\times \dfrac{5}{2}b[/tex]
[tex]\dfrac{6}{20}=b[/tex]
[tex]\dfrac{3}{10}=b[/tex]
Therefore, the width of the land is [tex]\dfrac{3}{10}[/tex] miles.