Consider the problem, A rod of length 20m is bent to make a rectangle. If its length is 2m more than breadth, find its length and breadth
Answers
Find the perimeter of each of the following figures:
Class_6_Mensuration_To_Find_Perimeter_Of_Different_Shapes1
Answer:
(a) Perimeter = Sum of all the sides
= 4 cm + 2 cm + 1 cm + 5 cm = 12 cm
(b) Perimeter = Sum of all the sides
= 23 cm + 35 cm + 40 cm + 35 cm = 133 cm
(c) Perimeter = Sum of all the sides
= 15 cm + 15 cm + 15 cm + 15 cm = 60 cm
(d) Perimeter = Sum of all the sides
= 4 cm + 4 cm + 4 cm + 4 cm + 4 cm = 20 cm
(e) Perimeter = Sum of all the sides
= 1 cm + 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm = 15 cm
(f) Perimeter = Sum of all the sides
= 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm +
1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm = 52 cm
Question 2:
The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?
Answer:
Total length of tape required = Perimeter of rectangle
= 2(length + breadth)
= 2(40 + 10)
= 2 * 50
= 100 cm
= 1 m {Since 1 m = 100 cm}
Thus, the total length of tape required is 100 cm or 1 m.
Question 3:
A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?
Answer:
Length of table top = 2 m 25 cm = 2 m + 0.25 cm = 2.25 m
Breadth of table top = 1 m 50 cm = 1m + 0.50 m = 1.50 m
Perimeter of table top = 2(length + breadth)
= 2(2.25 + 1.50)
= 2 * 3.75
= 7.50 m
Thus, the perimeter of table top is 7.5 m.
Question 4:
What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
Answer:
Length of wooden strip = Perimeter of photograph
Perimeter of photograph = 2(length + breadth)
= 2(32 + 21)
= 2 * 53 cm
= 106 cm
Thus, the length of the wooden strip required is equal to 106 cm.
Question 5:
A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?
Answer:
Since the 4 rows of wires are needed.
Therefore the total length of wires is equal to 4 times the perimeter of rectangle.
Perimeter of field = 2(length + breadth)
= 2(0.7 + 0.5)
= 2 * 1.2
= 2.4 km
= 2.4 * 1000 m
= 2400 m
Thus, the length of wire = 4 * 2400 = 9600 m = 9.6 km
Question 6:
Find the perimeter of each of the following shapes:
(a) A triangle of sides 3 cm, 4 cm and 5 cm.
(b) An equilateral triangle of side 9 cm.
(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm
Answer:
(a) Perimeter of triangle = Sum of all sides
= 3 cm + 5 cm + 4 cm
= 12 cm
(b) Perimeter of equilateral triangle = 3 * side
= 3 * 9 cm
= 27 cm
(c) Perimeter of isosceles triangle = Sum of all sides
= 8 cm + 6 cm + 8 cm
= 22 cm
Question 7:
Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
Answer:
Perimeter of triangle = Sum of all three sides
= 10 cm + 14 cm + 15 cm = 39 cm
Thus, the perimeter of triangle is 39 cm.
Question 8:
Find the perimeter of a regular hexagon with each side measuring 8 cm.
Answer:
Perimeter of Hexagon = 6 * length of one side
= 6 * 8
= 48 m
Thus, the perimeter of hexagon is 48 m.
Question 9:
Find the side of the square whose perimeter is 20 m.
Answer:
Perimeter of square = 4 * side
=> 20 = 4 * side
=> Side = 20/4
=> Side = 5 cm
Thus, the side of square is 5 cm.
Question 10:
The perimeter of a regular pentagon is 100 cm. How long is its each side?
Answer:
Perimeter of regular pentagon = 100 cm
=> 5 * side = 100 cm
=> Side = 100/5
=> Side = 20 cm
Thus, the side of regular pentagon is 20 cm.
Question 11:
A piece of string is 30 cm long. What will be the length of each side if the string is used to form: (a) a square (b) an equilateral triangle (c) a regular hexagon?
Answer:
Length of string = Perimeter of each figure
(a) Perimeter of square = 30 cm
=> 4 * side = 30 cm
=> side = 30/4 = 7.5 cm
Thus, the length of each side of square is 7.5 cm.
(b) Perimeter of equilateral triangle = 30 cm
=> 3 * side = 30 cm
=> side = 30/3 = 10 cm
Thus, the length of each side of equilateral triangle is 10 cm.
(c) Perimeter of hexagon = 30 cm
=> 6 * side = 30 cm
=> side = 30/6 = 5 cm
Thus, the side of each side of hexagon is 5 cm.
Question 12:
Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is the third side?
Answer:
Let the length of third side be x cm.
Lengths of other two sides are 12 cm and 14 cm.
Now, Perimeter of triangle = 36 cm
=> 12 + 14 + x = 36
=> 26 + x = 36
=> x = 36 - 26
=> x = 10 cm
Thus, the length of third side is 10 cm.
Question 13:
Find the cost of fencing a square park of side 250 m at the rate of Rs 20 per meter.
Answer:
Side of square = 250 m
Perimeter of square = 4 * side
= 4 * 250
= 1000 m
Since, cost of fencing of per meter = Rs 20
Therefore, the cost of fencing of 1000 meters = 20 * 1000 =