Question

the length and breadth of a rectangular piece of land are in the ratio 5 ratio 3 if the total cost of fencing it at rupees 24 is 9600 find its length and breadth ​

Answer 1

AnswEr :

• Length : Breadth = 5 : 3
• Total Cost of Fencing of Rectangular land @Rs. 24 per unit is Rs. 9600
• Find Length and Breadth.

Let the Length be 5x, and Breadth be 3x.

• Let's Head to the Question Now :

⇒ Total Cost = Perimeter × Rate

⇒ 9600 = 2 × (Length + Breadth) × 24

⇒ 9600 = 48 × (Length + Breadth)

• Dividing both term by 48

⇒ 200 = (5x + 3x)

⇒ 200 = 8x

• Dividing both term by 8

⇒ x = 25

_______________________________

• D I M E N S I O N S :

◗ Length = 5x = 5(25) = 125 unit

◗ Breadth = 3x = 3(25) = 75 unit

∴ Length and Breadth of the rectangular land is 125 unit and 75 unit respectively.

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• V E R I F I C A T I O N :

↠ Total Cost = Perimeter × Rate

↠ 9600 = 2 × (Length + Breadth) × Rate

↠ 9600 = 2 × (125 + 75) × 24

↠ 9600 = 2 × 200 × 24

↠ Rs. 9600 = Rs. 9600 ⠀Hence, Verified!

Answer 2

$\bold{\Huge{\underline{\boxed{\sf{\orange{ANSWER\::}}}}}}$

$\bold{\Large{\underline{\sf{\green{Given\::}}}}}$

The length & breadth of a rectangular piece of land are in the ratio 5:3, if the total cost of fencing it at Rs.24 is 9600.

$\bold{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The length & breadth.

$\bold{\Large{\underline{\sf{\purple{Explanation\::}}}}}$

Let the ratio be R.

$\bold{We\:have}\begin{cases} \sf{The\:length \:of \:rectangular \:piece=5R}\\ \sf{The\:breadth \:of \:rectangular \:piece=3R}\\ \sf{Cost \:of\: fencing=Rs.9600}\\ \sf{The\:rate\:per\:unit=Rs.24}\end{cases}$

Perimeter of rectangular piece= $\bold{\frac{Cost\:of\:fencing}{Rate\:per\:unit} }$

Perimeter of rectangular piece= $\bold{\cancel{\frac{9600}{24} }}$

Perimeter of rectangular piece= 400 units

Therefore,

We know that formula of the perimeter of rectangle:

→ 2(Length + Breadth)

→ 2(5R + 3R) = 400

→ 2(8R) = 400

→ 16R = 400

→ R = $\bold{\cancel{\frac{400}{16} }}$

→ R = 25 units

Thus,

●The length of a rectangular piece of land= 5(25)= 125 units.

●The breadth of a rectangular piece of land= 3(25)= 75 units.