Ex.3.2 Q5 Pair of Linear Equations in Two Variables Solution - NCERT Maths Class 10

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Question

Half the perimeter of a rectangular garden, whose length is \(4 \,\rm{m}\) more than its width, is \(36\,\rm{ m.}\) Find the dimensions of the garden.

 Video Solution
Pair Of Linear Equations In Two Variables
Ex 3.2 | Question 5

Text Solution

What is Known?

(i) Half the perimeter of rectangular garden \( = 36{\rm{\,m }}\)

(iii) Length is \(4{\rm{ \,m}}\) more than width

What is Unknown?

Dimensions of the garden

Reasoning:

Assuming length of the garden as \(x\) and width of the garden as \(y,\) two linear equations can be formed for the known data.

Perimeter of rectangle \(=\) 2(Length \(+\) Breadth)

Steps:

Let the length of the garden be \(x\) and breadth be \(y\)

Then \(x = y + 4\)

\[\begin{align}x - y &= 4\\y &= x - 4\end{align}\]

\(x\) \(8\) \(16\)
\(y = x - 4\) \(4\) \(12\)

Half perimeter of the rectangle be \(x + y = 36\)

\(y = 36 - x\)

\(x\) \(16\) \(26\)
\(y = x - 4\) \(20\) \(10\)

The answer is 

Length \(x = 20{\rm{\; m}}\)

Breadth \(y = 16{\rm{\; m}}\)