NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.1 Question 5

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables

Question:

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Given:

  • Let the width of the garden be \( x \) m.
  • Length of the garden is \( x + 4 \) m.
  • Half the perimeter is 36 m.

To Find:

  • The length and width of the garden.

Formula:

  • Perimeter of a rectangle \( = 2 \times (\text{Length} + \text{Width}) \)
  • Half perimeter \( = \text{Length} + \text{Width} \)

Solution:

Step 1: Let the width of the garden be \( x \) m. Then, the length is \( x + 4 \) m.

$$ \text{Width} = x \text{ m} \\ \text{Length} = x + 4 \text{ m} $$

Step 2: According to the question, half the perimeter is 36 m. So,

$$ \text{Length} + \text{Width} = 36 \\ x + (x + 4) = 36 $$

Step 3: Simplify the equation.

$$ x + x + 4 = 36 \\ 2x + 4 = 36 $$

Step 4: Subtract 4 from both sides.

$$ 2x + 4 - 4 = 36 - 4 \\ 2x = 32 $$

Step 5: Divide both sides by 2 to get the value of \( x \).

$$ \frac{2x}{2} = \frac{32}{2} \\ x = 16 $$

Step 6: Find the length using \( x \).

$$ \text{Length} = x + 4 = 16 + 4 = 20 \text{ m} $$

Result:

The dimensions of the garden are:

  • Width = 16 m
  • Length = 20 m
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