Question

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

Answer 1

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