Answer:
The area of the gazing land is [tex]\frac{30x-x^2}2[/tex] square miles.
Step-by-step explanation:
Given that, 30 miles of fencing can be used to enclose a rectangular piece of grazing land along a straight piece of river.
Let the length of the rectangular piece of gazing which is along the river be y and the width of the rectangular piece of gazing be x.
Along the river side, no fence is required.
Therefore total length of fence is = 2(x+y)-x
=2y+x
∴2y+x=30
⇒2y=30-x
[tex]\Rightarrow y=\frac{30-x}{2}[/tex]
The area of the rectangular piece of gazing is = Length×width
=xy
[tex]=x.\frac{30-x}2[/tex]
[tex]=\frac{30x-x^2}2[/tex] square miles.
