REVISION WORKSHEET
GRADE: VII
SUBJECT: MATHEMATICS
TOPIC: L-5,14,15

and represent two vertically opposite angles. Find the measure of each of the two angles.

In a triangle, the greatest angle is more than twice the middle angle and the smallest angle is less than the middle angle. Find all the angles of the triangle. What type of triangle is it?

After 12 years, Soumya shall be three times as old as she was 4 years ago. Find her present age.

The numerator of a fraction is 6 more than the denominator. If 5 is subtracted from the denominator, the fraction becomes . Find the fraction.

is a solution to which of the two equations?
a) .
b)

In a 100 marks test, each question carries 4 marks. Each correct answer gets 4 marks, and 1 mark is deducted for every wrong answer. If Mohina attempted all the questions and got 80 marks, find the number of correct answers in her test.

Find the root of the following equations and verify your answer:
a)
b)

Jaya and her 4 friends went to watch a movie in a theatre. They spent $₹$ per ticket and shared a tub of popcorn costing $₹$ . Find the amount shared by each one of them.

Chapter 14: AREA AND PERIMETER
1.The perimeter of one square is 24 m and that of another square is 32 m . Find the side of a square whose area is equal to the sum of areas of the two squares.
2. A 2.5 cm wide strip is cut from all around a rectangular sheet of paper of dimensions 25 cm by 15 cm . Find the area of the remaining sheet of paper.
3. A rectangular field measures 154 m by 20 m . How long will it take for a girl to go around the field if she walks at 12 m per minute?
4. The total cost of flooring a rectangular room at the rate of $₹$ per is 5640 . What is the area of the floor?
5.The perimeter of a rhombus is 24 cm , and its area is . Find its altitude.
6. Arjun’s mother is making a sandwich for him. She divides a square slice of bread with a side 12 cm diagonally into two equal halves. On one of the halves, she puts butter and on the other half, she puts jam. Find the area filled with butter.
7. How many parallelogram-shaped tiles with base 140 cm and height 60 cm can be put on a rectangular floor with dimensions ?
8. Find the cost of polishing a parallelogram-shaped table at $₹$ per if the base and corresponding altitude are 4.2 m and 2.5 m respectively.

Asked by an UpStudy premium member to our live tutor.

Jan 04,2025

Question

REVISION WORKSHEET
GRADE: VII
SUBJECT: MATHEMATICS
TOPIC: L-5,14,15

and represent two vertically opposite angles. Find the measure of each of the two angles.

In a triangle, the greatest angle is more than twice the middle angle and the smallest angle is less than the middle angle. Find all the angles of the triangle. What type of triangle is it?

After 12 years, Soumya shall be three times as old as she was 4 years ago. Find her present age.

The numerator of a fraction is 6 more than the denominator. If 5 is subtracted from the denominator, the fraction becomes . Find the fraction.

is a solution to which of the two equations?
a) .
b)

In a 100 marks test, each question carries 4 marks. Each correct answer gets 4 marks, and 1 mark is deducted for every wrong answer. If Mohina attempted all the questions and got 80 marks, find the number of correct answers in her test.

Find the root of the following equations and verify your answer:
a)
b)

Jaya and her 4 friends went to watch a movie in a theatre. They spent $₹$ per ticket and shared a tub of popcorn costing $₹$ . Find the amount shared by each one of them.

Chapter 14: AREA AND PERIMETER
1.The perimeter of one square is 24 m and that of another square is 32 m . Find the side of a square whose area is equal to the sum of areas of the two squares.
2. A 2.5 cm wide strip is cut from all around a rectangular sheet of paper of dimensions 25 cm by 15 cm . Find the area of the remaining sheet of paper.
3. A rectangular field measures 154 m by 20 m . How long will it take for a girl to go around the field if she walks at 12 m per minute?
4. The total cost of flooring a rectangular room at the rate of $₹$ per is 5640 . What is the area of the floor?
5.The perimeter of a rhombus is 24 cm , and its area is . Find its altitude.
6. Arjun’s mother is making a sandwich for him. She divides a square slice of bread with a side 12 cm diagonally into two equal halves. On one of the halves, she puts butter and on the other half, she puts jam. Find the area filled with butter.
7. How many parallelogram-shaped tiles with base 140 cm and height 60 cm can be put on a rectangular floor with dimensions ?
8. Find the cost of polishing a parallelogram-shaped table at $₹$ per if the base and corresponding altitude are 4.2 m and 2.5 m respectively.

Asked by an UpStudy premium member to our live tutor.

Jan 04,2025

UpStudy AI · Accepted Answer

Let's solve each problem step by step.

### Problem 1
Given two vertically opposite angles:
$$
(3x + 70)^{\circ} \quad \text{and} \quad (x + 100)^{\circ}
$$
Since they are vertically opposite, they are equal:
$$
3x + 70 = x + 100
$$
Now, let's solve for $$ x $$:
$$
3x - x = 100 - 70
$$
$$
2x = 30
$$
$$
x = 15
$$
Now, substitute $$ x $$ back to find the angles:
$$
(3(15) + 70)^{\circ} = 45 + 70 = 115^{\circ}
$$
$$
(15 + 100)^{\circ} = 115^{\circ}
$$
Thus, both angles are $$ 115^{\circ} $$.

### Problem 2
Let the middle angle be $$ x $$. Then:
- Greatest angle: $$ 2x + 20 $$
- Smallest angle: $$ x - 40 $$

The sum of angles in a triangle is $$ 180^{\circ} $$:
$$
x + (2x + 20) + (x - 40) = 180
$$
Simplifying:
$$
4x - 20 = 180
$$
$$
4x = 200
$$
$$
x = 50
$$
Now, find all angles:
- Middle angle: $$ 50^{\circ} $$
- Greatest angle: $$ 2(50) + 20 = 120^{\circ} $$
- Smallest angle: $$ 50 - 40 = 10^{\circ} $$

The angles are $$ 10^{\circ}, 50^{\circ}, 120^{\circ} $$. This is an obtuse triangle.

### Problem 3
Let Soumya's present age be $$ x $$. After 12 years, her age will be $$ x + 12 $$, and 4 years ago, her age was $$ x - 4 $$. According to the problem:
$$
x + 12 = 3(x - 4)
$$
Expanding:
$$
x + 12 = 3x - 12
$$
Rearranging:
$$
12 + 12 = 3x - x
$$
$$
24 = 2x
$$
$$
x = 12
$$
Soumya's present age is $$ 12 $$ years.

### Problem 4
Let the denominator be $$ x $$. Then the numerator is $$ x + 6 $$. The fraction is:
$$
\frac{x + 6}{x}
$$
If 5 is subtracted from the denominator:
$$
\frac{x + 6}{x - 5} = \frac{3}{2}
$$
Cross-multiplying:
$$
2(x + 6) = 3(x - 5)
$$
Expanding:
$$
2x + 12 = 3x - 15
$$
Rearranging:
$$
12 + 15 = 3x - 2x
$$
$$
27 = x
$$
Thus, the denominator is $$ 27 $$ and the numerator is $$ 33 $$. The fraction is:
$$
\frac{33}{27} = \frac{11}{9}
$$

### Problem 5
To check which equation $$ x = -2 $$ satisfies:
1. For $$ 3x + 7 = 13 $$:
   $$
   3(-2) + 7 = -6 + 7 = 1 \quad \text{(not equal to 13)}
   $$
2. For $$ -3x + 7 = 13 $$:
   $$
   -3(-2) + 7 = 6 + 7 = 13 \quad \text{(equal to 13)}
   $$
Thus, $$ x = -2 $$ is a solution to the second equation.

### Problem 6
Let $$ c $$ be the number of correct answers. The number of wrong answers is $$ q = \frac{80 - 4c}{1} $$. The total questions attempted is:
$$
c + q = \frac{80 + c}{4}
$$
Setting up the equation:
$$
c + \frac{80 - 4c}{1} = \frac{80 + c}{4}
$$
Multiplying through by 4:
$$
4c + 320 - 16c = 80 + c
$$
Rearranging:
$$
-12c + 320 = 80 + c
$$
$$
-13c = -240
$$
$$
c = 20
$$
Thus, Mohina got $$ 20 $$ correct answers.

### Problem 7
a) Solve $$ 2(3a + 1) = 12 + 2(4a + 3) $$:
$$
6a + 2 = 12 + 8a + 6
$$
$$
6a + 2 = 18 + 8a
$$
$$
2 - 18 = 8a - 6a
$$
$$
-16 = 2a \quad \Rightarrow \quad a = -8
$$

b) Solve $$ 7(y - 2) - 4(5 - y) = 10 $$:
$$
7y - 14 - 20 + 4y = 10
$$
$$
11y - 34 = 10
$$
$$
11y = 44 \quad \Rightarrow \quad y = 4
$$

### Problem 8
Total cost for tickets:
$$
5 \times 210 + 85 = 1050 + 85 = 1135
$$
Amount shared by each:
$$
\frac{1135}{5} = 227
$$

### Chapter 14: Area and Perimeter
1. Perimeter of square 1: $$ 24 \Rightarrow s_1 = 6 $$
   Perimeter of square 2: $$ 32 \Rightarrow s_2 = 8 $$
   Area of square 1: $$ 36 $$, Area of square 2: $$ 64 $$
   Total area: $$ 100 $$
   Side of square: $$ \sqrt{100} = 10 $$

2. Area of remaining sheet:
   Original area: $$ 25 \times 15 = 375 $$
   Area of strip: $$ (25 - 5)(15 - 5) = 20 \times 10 = 200 $$
   Remaining area: $$ 375 - 200 = 175 $$

3. Perimeter of field: $$ 2(154 + 20) = 348 $$
   Time to walk around: $$ \frac{348}{12} = 29 $$
1. Both angles are $$115^{\circ}$$. 2. The angles are $$10^{\circ}$$, $$50^{\circ}$$, and $$120^{\circ}$$. It's an obtuse triangle. 3. Soumya is 12 years old now. 4. The fraction is $$\frac{11}{9}$$. 5. $$x = -2$$ is a solution to the second equation. 6. Mohina got 20 correct answers. 7. a) $$a = -8$$ b) $$y = 4$$ 8. Each person shared $$₹227$$. 9. The side of the square is 10 meters. 10. The remaining area is $$175 \, \text{cm}^2$$. 11. It takes 29 minutes to walk around the field. 12. The area of the floor is $$60 \, \text{sq. m}$$. 13. The altitude of the rhombus is $$8 \, \text{cm}$$. 14. The area filled with butter is $$6 \, \text{cm}^2$$. 15. 140 tiles can be placed on the floor. 16. The cost of polishing the table is $$₹67.20$$.

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