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

## 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.

## 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

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

\(x\) | \(8\) | \(16\) |

\(y = x - 4\) | \(4\) | \(12\) |

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