Page 184 - classs 6 a_Neat

or ad= be
that is, the product of the extremes = the product of the means If a, b, c are in continued proportions, then a:b : : 13 Concept of Perimeter
b:c and ac =b 2 and Area
In continued proportion, the second term is called the mean proportion as the second and third terms are the
same. The fourth terms is called the third proportion. PERIMETER OF A PLANE FIGURE The sum of the lengths of all sides of a plane figure, or the length of its
The unitary method is the method of finding the value of a single item. The values of the desired quantity can boundary, is called the perimeter o.[ the figure.
then be found out.
PERIMETER OF A RECTANGLE Perimeter of a rectangle
= 2(length + breadth)
= 2(l + b) units.

PERIMETER OF A SQUARE Perimeter of a square
= (4 x side)= (4a) units.

SOLVED EXAMPLES

EXAMPLE 1. Find the perimeter of a rectangle whose length and breadth are 15.4 cm and 11.6 cm
respectively.
SOLUTION Length of the rectangle = 15.4 cm.
Breadth of the rectangle = 11.6 cm.
Perimeter of the rectangle = 2 (l + b) units
= 2(15.4+11.6) cm= (2 × 27) cm= 54 cm.
Hence, the perimeter of the rectangle is 54 cm.
EXAMPLE 2. Find the cost of fencing a rectangular field 260 m long and 175 m wide at 40 permetre.
SOLUTION Length of the field = 260 m.
Breadth of the field = 1 75 m.
Perimeter of the field = 2 (l + b) units
= 2(260 +175) m = (2 × 435) m = 870 m.
Cost of fencing per metre = 40.
Total cost of fencing = ₹ (870 × 40) = ₹ 34800
EXAMPLE 3. The length and the breadth of a rectangular field are 240 m and 180 m respectively. It
is fenced with three rounds of a rope. Find the length of the rope.
SOLUTION Length of the field = 240 m and its breadth = 180 m.
Perimeter of the field = 2 x (length + breadth) units
= {2 × (240 +180)} m = (2 × 420) m = 840 m.
Total length of rope == (3 × 840) m = 2520 m.
EXAMPLE 4. The length and the breadth of a rectangle are in the ratio 3 : 2. if its perimeter ts
1 m 40 cm.find its dimensions.
SOLUTION Let the length of the rectangle be 3x cm.
Then, its breadth = 2x cm.
∴ perimeter of the rectangle = {2x (length+ breadth)} units
∴ length= (3 × 14) cm = 42 cm and breadth= (2 × 14) cm = 28 cm.
EXAMPLE 5. The cost of fencing a rectangular field at ` 24 per metre is ₹1920. if its length is 23m,
find its breadth.
SOLUTION Total cost of fencing = ₹1920.
Rate of fencing = ₹ 24 per metre.

Perimeter of the field=    totalcos t  = `1920
 rate  ` 24 / m