3'. (a) Find the value of abc - ab - bc for a=2,b=-3 and c=-1.
(b) Vipin is 42 years old and his son is 12 years old. After how many years will Vipin's age be twice that
of his son?
4. (a) Draw a triangle with three lines of symmetry.
(b) The cost of wall-to-wall carpeting of the floor of a room is Rs 24000. If the room is 20 m long and the
carpet costs Rs 100 per sq. m, find the breadth of the room.
OR
4'. (a) Construct a quadrilateral with:
(i) two lines of symmetry (ii) four lines of symmetry
(b) Write any four alphabets having two line of symmetry.
5. (a) If the perimeter of a rhombus is 40 m, find the length of its side.
(b) How much will it cost to plough a field 34 m by 26 m at the rate of Rs 12 per sq. m?
OR
5'. (a) Express the given number using tally marks.
(i) 28 (ii) 32 (iii) 16 (iv) 22
Answers
Answer:
members watching this question
Step-by-step explanation:
1. As a
3
+b
3
+c
3
−3abc=(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
⇒(a
3
+b
3
+c
3
−abc)=(a+b+c)[(a+b+c)
2
−3(ab+bc+ca)]
⇒(a
3
+b
3
+c
3
−3abc)=9[81−78]=27
2.Let the number of years be x.
Therefore the age of son would be 12+x whereas the age of father would be 42+x.
And it is given that the age of father would be twice of the son(same as the age of the son be half of the age of the man), therefore,
2(12+x)=42+x
24+2x=42+x
2x−x=42−24
x=18
Hence, the number of years is 18.
3.
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Class 9
>>Maths
>>Surface Areas and Volumes
>>Surface Area of Cubes and Cuboids
>>The length, breadth and height of a room
Question
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The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost white washing the walls of the room and ceiling at the rate of Rs. 7.50 per m
2
.
Medium
Solution
verified
Verified by Toppr
Given:
L=5 m, B=4 m, H=3m
⇒Area to be white-washed = Area of cuboid − Area of base.
=2lh+2bh+2lb−lb
=2lh+2bh+lb
=[2×5×3+2×4×3+5×4]m
2
=74m
2
Cost of white washing per m
2
area = Rs.7.50
Cost of white washing 74m
2
area=74×7.50
= Rs.555
4. search-icon-image
Question
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The perimeter of a rhombus is 40 cm and the length of one of its diagonals is 12 cm then the area of the rhombus is
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Given the perimeter of rhombus is 40 cm and one diagonal is 12 cm
We know that perimeter of rhombus=2
p
2
+q
2
where -p and q are diagonal of rhombus
∴40=2
(12)
2
+q
2
⇒20=
144+q
2
⇒400=144+q
2
⇒q
2
=400−144=256
⇒q=16 cm
Then length of second diagonal is 16 cm
Then area of rhombus=
2
p×q
=
2
12×16
=
2
192
=96Cm