# Ex.11.1 Q1 Mensuration Solutions - NCERT Maths Class 8

## Question

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

## Text Solution

**What is Known?**

Perimeter of rectangular field and square area same and also one side of square and rectangular field are known.

**What is unknown?**

Breadth of rectangular field .

Area of square and rectangular field.

**Reasoning:**

It is given that perimeter of the square and the rectangular field are same, so we can find breadth of the rectangular field and also the area of the rectangular field.

**Steps:**

Side of the square \(= 60\rm\,m\)

Length of the rectangle \(= 80\rm\,m\)

Perimeter of the square \( \begin{align} &= 4 \times {\text{side of square}}\\ &= 4 \times 60 {\rm{m}} = 240 {\rm{m}} \end{align}\)

Perimeter of rectangle \( = 2 \times ({\rm{length}} + {\rm{breadth}})\)

Perimeter of square \(=\) Perimeter of rectangle

\[\begin{align}240 &= \! 2\! \times \!( \! {\rm{length}} \!+\! {\rm{breadth}}\!)\\240 &= 2 \times (80 + {\rm{breadth}})\\240 &= 160 + 2 \times {\rm{breadth}}\\240 - 160 &= 2 \times {\rm{breadth}}\\{\rm{80 }}&= 2 \times {\rm{breadth}}\end{align}\]

\[{\rm{breadth}} = \frac{{80}}{2} = 40\rm\,m\]

Area of the square

\[\begin{align} &= {\rm{side}} \times {\rm{side}} \\ &= 60 \times 60 \\ &= 3600{{\rm{m}}^2}\end{align}\]

Area of the rectangular field

\[\begin{align} &= {\rm{length}} \times {\rm{breadth}}\\ &= 80 \times 40 = 3200{{\rm{m}}^2}\end{align}\]

Thus, area of square is larger than the area of rectangular field.