Question

the ratio of the length and breath of rectangular plot is 11:4 the cost of fencing the plot at the rate of rupees 100 per metre is rupees 15000 . find the dimensions of the plot

Answer 1

Hey there !

Thanks for the question !

Solution:

Given Information:

• Length : Breadth = 11 : 4
• Cost of Fencing = Rs. 15000 ( Rs. 100 per m² )

To Find:

• Dimensions of the Plot

Illustration:

Let the ratio of length and breadth be 11x : 4x respectively.

So Fencing refers to Perimeter of the plot

So Perimeter = 2 ( l + b ) as it is a rectangular plot.

Also we know that,

Perimeter × Cost per m² = Total Cost

=> Perimeter × 100 = 15000

=> Perimeter = 15000 / 100 = 150 m

Hence the perimeter is 150 m.

So Perimeter of Rectangular Plot = 2 ( l + b )

We know 'l' = 11 x and 'b' = 4x

So 2 ( 11x + 4x ) = 150

=> 2 ( 15 x ) = 150

=> 30 x = 150

=> x = 150 / 30

=> x = 5

Hence the value of 'x' is 5.

So Length = 11 x = 11 × 5 = 55 m

Breadth = 4 x = 4 × 5 = 20 m

Hence the dimensions are 55 m and 22 m.

Hope my answer helped !

Answer 2

Ratio = 11 : 4 (Given)

Cost = Rs 15 000 (Given)

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STEP 1: Find the perimeter in x:

Let the constant ratio be x

Length : Breath = 11x : 4x

Perimeter = 2 (Length + Breadth)

Perimeter = 2 (11x + 4x)

Perimeter = 2 (15x)

Perimeter = 30x

........................................................................................................................

STEP 2: Find the value of x:

30x = 15 000

x = Rs 500

........................................................................................................................

STEP 3: Find the cost of Length and Breadth

Length = 11x = 11(500) = Rs 5500

Breadth = 4x = 4(500) = Rs 2000

........................................................................................................................

STEP 4: Find the dimension:

Rs 100 = 1 m (Given)

Length = Rs 5500

Length = 5500 ÷ 100 = 55 m

Breadth = 2000 ÷ 100 = 20 m

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Answer: Length = 55 m and Breadth = 20 m