Answer:
The length and breadth of the fence are 80 and 70 meters, respectively.
Step-by-step explanation:
Let suppose that fencing has a rectangular form. The length to breadth ratio is [tex]\frac{8}{7}[/tex]. Dimensionally speaking, the total cost for fencing the plot ([tex]C[/tex]), measured in monetary units, is the product of perimeter of the rectangle ([tex]p[/tex]), measured in meters, and unit cost ([tex]c[/tex]), measured in monetary units per meter, that is:
[tex]C = c\cdot p[/tex] (1)
[tex]C = 2\cdot c\cdot (w+l)[/tex] (2)
Where:
[tex]w[/tex] - Breadth of the fence, measured in meters.
[tex]l[/tex] - Length of the fence, measured in meters.
By applying the ratio described above, we reduce (2) into this form:
[tex]C = 2\cdot c\cdot \left(\frac{1}{r} +1\right)\cdot l[/tex] (3)
Where [tex]r[/tex] is the length to breadth ratio, no unit.
If we know that [tex]C = 60000[/tex], [tex]c = 200[/tex] and [tex]r = \frac{8}{7}[/tex], then the length and breadth of the rectangle are, respectively:
[tex]l = \frac{C}{2\cdot c\cdot \left(\frac{1}{r} +1\right)}[/tex]
[tex]l = \frac{60000}{2\cdot (200)\cdot \left(\frac{7}{8}+1 \right)}[/tex]
[tex]l = 80\,m[/tex]
[tex]w = \frac{l}{r}[/tex]
[tex]w = \frac{80\,m}{\frac{8}{7} }[/tex]
[tex]w = 70\,m[/tex]
The length and breadth of the fence are 80 and 70 meters, respectively.
