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