Math, asked by madhurmodi888, 1 month ago

The breadth of a rectangular garden is 23 of its length.
If its perimeter is 40 m, find its dimensions.

Answers

Answered by george0096
10

Correct Question:

  • The breadth of a rectangular garden is 2/3 of its length.  If its perimeter is 40 m, find its dimensions.

Answer:

  • The length and breadth of the garden are 12 m and 8 m respectively.

Step-by-step explanation:

Given that:

  • The breadth of a rectangular garden is 2/3 of its length.
  • The perimeter of the rectangular garden is 40 m.

To Find:

  • The dimensions of the rectangular garden.

Let us assume:

  • The length of the rectangular garden be x.

Then,

  • The breadth of the garden will be 2x/3.

As we know that:

  • Perimeter of rectangle = 2(length + breadth) units

Substituting the values,

\sf{\implies40=2\left(x+\dfrac{2x}{3}\right)}

Solving the bracket,

\sf{\implies40=2\left(\dfrac{2x+3x}{3}\right)}

\sf{\implies40=2\left(\dfrac{5x}{3}\right)}

Opening the bracket,

\sf{\implies40=2\times\dfrac{5x}{3}}

Multiplying RHS,

\sf{\implies40=\dfrac{10x}{3}}

Transposing 3 from RHS to LHS and changing its sign,

\sf{\implies40\times3=10x}

Multiplying LHS

\sf{\implies120=10x}

Transposing 10 from RHS to LHS and changing its sign,

\sf{\implies\dfrac{120}{10}=x}

Dividing LHS,

\sf{\implies12=x}

Hence,

  • x = 12

Therefore,

  • Length of the garden = x = 12 m
  • Breadth of the garden = 2x/3 = (12 × 2)/3 = 8 m

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