Question

14. A rectangular area of 9000 m2 is to be surrounded by a fence with two opposite sides
being made of bricks and the other two of wood. One metre of wooden fencing costs
25 rupees while one metre of brick walling, costs 10 rupees
. What is the least amount of money that must
be allotted for the construction of such a fence?​

Answer 1

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Answer 2

Answer:

The least amount of money that must be allotted for the construction of such a fence is 6000 rupees.

Step-by-step explanation:

It is given that area of rectangular portion is 9000.

It is decided to cover the rectangular area by a fence with two opposite sides being made of bricks and the other two of wood.

Cost of one meter of wooden fencing is 25 rupees.

Cost of one meter of brick walling, 10 rupees.

It is asked to find the least amount of money that must be allotted for the construction of such a fence.

Here, let the length of rectangular area be l and breadth be b.

Area, $l*b=9000$

$l=\frac{9000}{b}$

Total cost, $C=2(l*10+b*25)$

Multiplied by 2 for both the sides.

We need to find minimum C.

$C=2(\frac{9000}{b} *10+b*25)$

Differentiating C with respect to b and equating to 0.

$2(-\frac{9000}{b^2}*10+25)=0$

$\frac{9000}{b^2}*10=25$

$b^2=\frac{90000}{25} =3600$

$b=60$

$l=\frac{9000}{60}=150$

The length is 150 and breadth is 60.

Total cost, $C=2(l*10+b*25)$

$C=2(150*10+60*25)$

$C=2(1500+1500)$

$C=2(3000)=6000$

The least amount of money needed is 6000 rupees.

To know more about area go to the following link.

https://brainly.in/question/28136612

To have more problems of cost of fence go to the following link.

https://brainly.in/question/13821012

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