# Ex.11.1 Q7 Perimeter and Area - NCERT Maths Class 7

## Question

The perimeter of a rectangle is \(130 \,\rm{}cm.\) If the breadth of the rectangle is \(30 \,\rm{}cm, \) find its length. Also find the area of the rectangle.

## Text Solution

**What is known?**

The perimeter and the breadth of the rectangle.

**What is unknown?**

Length and area of the rectangle.

**Reasoning:**

Since the perimeter and breadth of rectangle are given, we can find out the length of the rectangle. From the values of length and breadth, area of rectangle can be calculated.

**Steps:**

Given,

Breadth of the rectangle \(= 30 \,\rm{}cm\)

Perimeter of a rectangle \(= 130 \,\rm{}cm.\)

We know that,

\(\begin{align}&\text{Perimeter of rectangle} \\ &= 2 \times \left( {{\rm{Length}} + {\rm{Breadth}}} \right)\end{align} \)

\[\begin{align}130 &= 2 \times \left( {l + 30} \right)\\130 &= 2\,l + 60\\2\,l &= 130-60\\2\,l &= 70\\l &= \frac{{70}}{2}\\l &= 35\;\rm{cm}\end{align}\]

Area of rectangle

\[\begin{align}&=\text{ Length} \times\text{ Breadth} \\ & = 35 \times 30 \\ &= 1050 \,\rm{cm^2}\end{align} \]