All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3181
If the side of a square is doubled, how many times does its area increase?
Answer:
4 times
Let the original side be 's', so original area = s². If the side is doubled, the new side is '2s'. The new area = (2s)² = 4s². The new area is exactly 4 times the original area.
3182
The area of a rectangle is 120 cm². If its length is 15 cm, what is its perimeter?
Answer:
46 cm
First, find the width: Area = length * width, so 120 = 15 * width, meaning width = 8 cm. Next, calculate the perimeter: Perimeter = 2 * (length + width) = 2 * (15 + 8) = 2 * 23 = 46 cm.
3183
What is the area of a square whose diagonal is 10 cm long?
Answer:
50 cm²
The area of a square can be calculated directly from its diagonal (d) using the formula: Area = (d²) / 2. Substituting d = 10 cm: Area = (10²) / 2 = 100 / 2 = 50 cm².
3184
If the perimeter of a square is 64 cm, what is the length of one side?
Answer:
16 cm
A square has four equal sides. The perimeter is the sum of all four sides. Formula: Perimeter = 4 * side. Therefore, side = Perimeter / 4 = 64 / 4 = 16 cm.
3185
Find the length of the diagonal of a rectangle with sides 6 cm and 8 cm.
Answer:
10 cm
The diagonal of a rectangle forms a right-angled triangle with its length and width. By the Pythagorean theorem, Diagonal = √(length² + width²). Diagonal = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
3186
Calculate the perimeter of a rectangle whose length is 18 meters and width is 12 meters.
Answer:
60 m
The perimeter of a rectangle is the total distance around its outside edges. Formula: Perimeter = 2 * (length + width). Substituting the values: Perimeter = 2 * (18 + 12) = 2 * 30 = 60 m.
3187
What is the area of a rectangle with a length of 14 cm and a width of 9 cm?
Answer:
126 cm²
The area of a rectangle is calculated by multiplying its length by its width. Formula: Area = length * width. Substituting the given values: Area = 14 cm * 9 cm = 126 cm².
3188
The ratio of the base to the height of a triangle is 3:4. If its area is 150 cm², what is the length of its base?
Answer:
15 cm
Let the base be 3x and the height be 4x. Area = (1/2) * base * height = 150. So, (1/2) * 3x * 4x = 150, which simplifies to 6x² = 150. Dividing by 6 gives x² = 25, so x = 5. The base is 3x = 3 * 5 = 15 cm.
3189
A triangle has sides 7 cm, 24 cm, and 25 cm. What type of triangle is it?
Answer:
Right-angled triangle
Check if the sides satisfy the Pythagorean theorem (a² + b² = c²). Here, 7² + 24² = 49 + 576 = 625. Since 25² is also 625, the square of the longest side equals the sum of the squares of the other two sides, making it a right-angled triangle.
3190
Using Heron's formula, calculate the semi-perimeter (s) of a triangle with sides 8 cm, 15 cm, and 17 cm.
Answer:
20 cm
The semi-perimeter (s) of a triangle is half of its total perimeter. Formula: s = (a + b + c) / 2. Substituting the sides: s = (8 + 15 + 17) / 2 = 40 / 2 = 20 cm.