NCERT Solutions
Class 10 - Mathematics - Chapter 3: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - Exercise 3.1
Question 5

Question. 5

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.

Answer:

Let the length of the rectangular garden be \(l\) metres and the width be \(b\) metres.

Given that the length is 4 m more than the width:

\[ l = b + 4. \]

Perimeter of a rectangle is \(2(l + b)\). Half the perimeter is therefore \(l + b\).

It is given that half the perimeter is 36 m:

\[ l + b = 36. \]

So we have the system

\[ l = b + 4, \qquad l + b = 36. \]

Substitute \(l = b + 4\) in \(l + b = 36\):

\[ (b + 4) + b = 36 \Rightarrow 2b + 4 = 36 \Rightarrow 2b = 32 \Rightarrow b = 16. \]

Then

\[ l = b + 4 = 16 + 4 = 20. \]

Therefore, the dimensions of the garden are: length \(20\) m and breadth \(16\) m.

Detailed Answer with Explanation:

Translate the wording into two equations: one from “length is 4 m more” and one from the given half-perimeter. Substitute the first into the second to solve for width, then back-solve for length.

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