Respuesta :
Step-by-step explanation:
Let x be the length and y be the width of the rectangular plot.
The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,
x+2y = 1500
x = 1500 - 2y ....(1)
We know that the area of a rectangular plot is given by :
A = xy ....(2)
Put the value of x from equation (1) in (2)
[tex]A=(1500-2y)y\\\\A=1500y-2y^2[/tex] .....(3)
For largest area, differentiate above area equation wrt y.
[tex]\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375[/tex]
Put the value of y in equation (1).
x = 1500-2(375)
= 750 m
Put the value of y in equation (3).
[tex]A =1500(375)-2(375)^2\\A=281250\ m^2[/tex]
Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.
