Page 166 - Ganit Kaushal

Applications of Perimeter in Daily Life

We come across situations in daily life where we need to measure perimeter.
1. Fencing a Garden: If you want to put a fence around your garden to prevent trespassing, you need
to find how long the fence should be. Here, you calculate the perimeter.
2. Decorating a Photo Frame: If you want to stick a ribbon along the border of a photo frame, you
need to know how long the ribbon should be. You find the perimeter of the frame.
3. Walking Around a Playground: If you walk once around your playground, the distance you cover
is its perimeter.
Solved Examples

Ex 1. A farmer has a rectangular field with a length of 230 m and a breadth of 160 m. He wants to fence it
with 3 rounds of rope as shown. What is the total length of rope needed? (NCERT)
Sol. Perimeter of the farmer’s rectangular field
= 2(length + breadth)
= 2 × (230 m + 160 m) = 2 × 390 m = 780 m
Rope needed to fence the field once = 780 m 160 m 230 m
\ Rope needed for 3 rounds = 3 × 780 m = 2340 m
Ex 2. Find the missing terms:
(a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?
(b) Perimeter of a square = 20 cm; side of a length = ?

(c) Perimeter of a rectangle = 12 m; length = 3 m; breadth = ? (NCERT)
Sol. (a) Let the length of a rectangle be L.
Perimeter of rectangle = 2(length + breadth)
⇒ 2 × (L + 2 cm) = 14 cm ⇒ 2L + 4 cm = 14 cm ⇒ 2L = (14 – 4) cm
⇒ 2L = 10 cm ⇒ L = 5 cm.
(b) Let the length of the side of a square be L.
Perimeter of a square = 4 × length of a side

⇒ 4 × L = 20 cm ⇒ L = 20 ÷ 4 ⇒ L = 5 cm.
(c) Let the breadth of the rectangle be b.
\ 2 × (3 m + b) = 12 m ⇒ 6 m + 2b = 12 m ⇒ 2b = (12 – 6) m = 6 m
\ b = 6 ÷ 2 = 3 m.
Ex 3. Based on the adjoining picture, answer the 70 m
following questions. 60 m

(a) Find out the total distance Akshi has 40 m Akshi and Toshi start running along the rectangular
covered in 5 rounds. tracks as shown in the figure. Akshi runs along the
outer track and completes 5 rounds. Toshi runs along
(b) Find out the total distance Toshi has covered 30 m the inner track and completes 7 rounds. Now, they
are wondering who ran more. Find out who ran the
in 7 rounds. Who ran a longer distance? longer distance.

(c) Think and mark the positions as directed—
(i) Mark ‘A’ at the point where Akshi will
be after she has run 250 m. Starting Point Starting Point
for Toshi for Akshi

164 Mathematics-6