Question

area of a rectangular garden of length 40m is 1000 sqm find the breadth of the garden is to be enclosed by 3rounds of fencing, leaving an entrance of 4cm find the cost of fencing the garden at a rate of 250 rs per meter​

Answer 1

Answer :

Cost = ₹ 97,470

Breadth = 25 m

$\rule{100}2$

Given :

• Length of rectangular garden = 40 m
• Area = 1000 m²
• Area to be left for entrance = 4 cm

To Find :

• Breadth of the rectangular field
• Cost of fencing at the rate of ₹ 250 per meter.

SolUtion :

→ For Breadth,

By using the formula of Area of square,

$\sf Area=length\times breadth$

$\tt 1000=40\times breadth$

$\tt \implies breadth=\dfrac{1000}{40}$

$\tt \therefore breadth=25\: m$

Now,

Perimeter of rectangle = 2 ( length + breadth )

$\tt =2(40 + 25)$

$\tt = 2(65)$

$\tt=130\:m$

Total perimeter ⇒ 3 × 130 = 390 m

→ Leaving entrance area of 4 cm.

∵ 1 m = 100 cm, 4 cm = 0.04 m

Also, it is enclosed by 3 rounds. So, 3 × 0.04 = 0.12 m

Fence required,

Perimeter - Area to be left for entrance

$\tt 390 - 0.12$

$\tt = 389.88 \:$

Cost of fencing,

$\tt 389.88\times 250$

$\tt = 97,470$

Breadth of the rectangular garden is 25 m and the cost of fencing is ₹ 97, 470

$\rule{200}2$

Answer 2

Given,

• The area of Rectangular garden = 1000 m²
• Length of Rectangular garden  = 40 m
• Area to be leave an entrance = 4 m

To Find,

• The Cost of fencing the garden at a rate of ₹250 per metre.

Solution,

$\mapsto \sf{Firstly , \ Find \ the \ Breadth \ of \ Rectangle : }$

$\underline{\sf{\large{\pink{We \ Know \ that :}}}}$

$\implies \boxed{\sf{Area \ of \ Rectangle = Length \times Breadth }}$

$\implies \sf{40 \times Breadth = 1000}$

$\implies \sf{\therefore \ Breadth = \dfrac{1000}{40}}$

$\implies \boxed{\sf{Breadth = 25 \ m}}$

$\boxed{\sf{\purple{Now, \ Find \ Perimeter \ of \ Rectangle :}}}$

$\implies \sf{Perimeter \ of \ Rectangle = 2(40 + 25)}$

$\implies \sf{Perimeter \ of \ Rectangle = 2(65)}$

$\implies \boxed{\sf{Perimeter \ of \ Rectangle = 130 \ m}}$

$\sf{\underline{\red{Now, We \ Find \ the \ Total \ Perimeter \ of \ Rectangle :}}}$

$\implies \sf{ \therefore 3 \times 130 = \boxed{\sf{\red{390 \ m}}}}$

(Given that garden is to be enclosed by 3 rounds of fencing)

$\underline{\sf{\purple{Now, \ Find \ Leaving \ entrance \ Area :}}}$

$\implies \sf{Leaving \ entrance \ area = 4 \ cm }$

∵ We know that :- 1 m = 100 cm

∴4 cm = 0.04

║It is enclosed by 3 rounds so leaving entrance area in also include ║

$\implies \sf{\therefore 3 \times 0.04 = \boxed{\sf{\pink{0.12 \ m}}}}$

$\bold{\underline{\sf{\purple{According \ to \ the \ Question :}}}}$

$\boxed{\sf{Case - (i)}}$

• Perimeter After removing entrance Area

$\implies \sf{390 - 0.12 = \boxed{\sf{\pink{389.88 \ m }}}}$

$\boxed{\sf{Case - (ii)}}$

• Cost of fencing the garden at a rate of ₹250 per meter.

$\implies \sf{389.88 \times 250 = \boxed{\sf{\pink{97,470}}}}$

$\rule{200}2$