Session 1: Perimeter of Rectangle – Formula, Definition, Interactive and Examples

What is Perimeter?

Perimeter is the distance around a shape. In other words, the total boundary length of a closed two-dimensional figure is called its perimeter. The perimeter of a circle or ellipse is called its circumference. To find the perimeter of any two-dimensional shape, find the sum of the lengths of all the sides.

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Perimeter of Rectangle

A rectangle is a plane figure whose opposite sides (facing each other) are of equal lengths. So, we have two equal lengths (bases) and two equal heights (breadths). The perimeter of a rectangle is the total length of its boundary on all sides.

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Formula for Perimeter of Rectangle

Consider a rectangle shown below.

Let b and ℎ denote its base and height, respectively.

It follows from this formula that

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Perimeter of Rectangle – Examples

Example 1

Find the perimeter of a rectangle whose length is 24 cm and breadth is 15 cm.

We know,

Perimeter of a rectangle =2 (breadth + length)               

Example 2

Find the breadth of the rectangle whose length is 130 cm and perimeter 460 cm.

We know,

Perimeter of a rectangle =2 (breadth + length)

∴Breadth of the rectangle=\(\frac{Perimete{{r}_{rectangle}}}{2}\)−length                  

Example 3

Find the distance covered by an ant crawling along the edge of a rectangular tabletop.

The distance travelled by the ant is the perimeter of the rectangular region, i.e. the tabletop. The perimeter of the tabletop is 

Perimeter=2(120+70)
=2(190)
=380 cm

Example 4

The length and breadth of a rectangular park are in the ratio 5:2. If the perimeter is 490 m, what are its dimensions?

We know the two terms of the ratio.

Here the total number of parts are 5+2=7 parts.

If 7 parts =490, then 1 part =\(\frac{490}{7}\)=70 m.

Therefore, length =5 parts =5×70=350 m, which refers to the sum of lengths of two sides.

So, length of rectangular park=\(\frac{450}{2}\)=175 m.

Similarly, breadth =2 parts=2×70=140 m, which refers to the sums of breadths of two sides.

So, breadth of rectangular park =\(\frac{140}{2}\)=70 m.

Example 5

A rectangular park is 180 m by 140 m. Karthik walks around it at the rate of 3200 m per hour. In how much time will he make 10 rounds?

Distance covered in one round = Perimeter of the park         

∴ Distance covered in 10 rounds =640×10=6400 m.

∵ Kartik walks 3200 m in one hour,

∴ Kartik walks 6400 m in \(\frac{1}{3200}\)×6400=2 hours.

Remember this!

• Perimeter is the total boundary length of a closed two-dimensional figure.
• The formula for perimeter of a rectangle is: Perimeterrectangle=2(base+height)
• Using the formula for perimeter of a rectangle, we can find the base and height of the rectangle: 
  base=\(\frac{Perimete{{r}_{rectangle}}}{2}\)−height
  height=\(\frac{Perimete{{r}_{rectangle}}}{2}\)−base