Question

8. The length and breadth of a rectangular
piece of land are in the ratio of 4:3. If the
total cost of fencing it at 10 per metre is rupees 4200 find the length and breadth​

Answer 1

Answer:

Length = 12 m

Breadth = 9 m

Step-by-step explanation:

Given, for rectangular piece of land,

ratio of length and breadth = 4:3

cost of fencing = ₹ 10/sq. m

total cost of fencing = ₹ 4,200

Soln: Perimeter = total cost of fencing paid ÷ cost of fencing

= ₹ 4,200 / ₹ 10/sq. m

•°• P = 42 m

Let the length and breadth be 4x and 3x respectively.

°•° P = 2 (l + b)

42 m = 2 (4x + 3x)

42 = 2 × 7x

42 = 14x

14x = 42

x = 42 / 14

•°• x = 3

Hence, length = 4x = 4 (3) = 12 m.

breadth = 3x = 3 (3) = 9 m.

Adiós! Hope this helps you!

Answer 2

Given :

• Ratio of length and breadth of the rectangle = 4:3.
• Cost for fencing 1 meter = Rs.10.
• Total Cost for fencing = Rs.4200.

To Find :

• Find length and Breadth

Explanation :

• It's given that the rectangular piece of land has length and breadth in the ratio as 4:3. And given that cost of fencing 1 metre of land is Rs.10. And total cost for fencing is Rs.4200.
• Fencing is always be done in the Border of the land or garden or field, so we have to find the perimeter of the the rectangular piece of land.
• we have to find the perimeter of the rectangular piece of land tgen have to find the measures of length and breadth. lets have length as 4x and breadth as 3x

→ Total Cost for fencing = Cost for fencing 1 meter x Perimeter of the land.

$\displaystyle {\boxed{\sf{Perimeter \:Of \:the\: land = \frac{Total \:Cost \:for \:fencing}{ Cost\: for\: fencing \:1 \:meter.}}}}$

Formula Applied :

$\underline{\boxed{\sf{Perimeter_{(Rectangle)}= 2(l+b)}}}$

Solution :

• As by given explanation substitute the values in formula.

$\displaystyle {\sf{Perimeter \:Of \:the\: land = \frac{Total \:Cost \:for \:fencing}{ Cost\: for\: fencing \:1 \:meter.}}}$

$\implies\sf{\frac{4200}{10}}$

$\boxed{\sf{420 \:meters}}$

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• As by Explanation we have length as 4x and breadth as 3x. Substitute the values in the formula of perimeter of rectangle.

$\implies {\sf{Perimeter_{(Rectangle)}= 2(l+b)}}$

$\implies \sf{2(4x+3x)=420}$

$\implies \sf{2(7x)=420}$

$\displaystyle {\implies \sf{7x= \frac{420}{2}}}$

$\displaystyle {\implies \sf{x = \frac{210}{7}}\implies x = 30}$

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• Now substitute the value of x in indirect value of length and breadth.

$\implies \sf{Length = 4x}$

$\implies \sf{4(30)}$

$\boxed{ \sf{Length= 120m}}$

$\implies \sf{Breadth= 3x}$

$\implies \sf{3(30)}$

$\boxed{ \sf{Breadth = 90m}}$

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Required Answer :

• Length of the rectanglular piece of land is $\underline {\sf{Length= 120m}}$
• Breadth of the rectangular piece of land is $\underline{\sf{Breadth = 90m}}$

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