- 10 √2 cm
- 40 cm
- 200 cm
- 40 √2 cm

**Correct Answers Is: 4**

**SOLUTION**

**Given:**

The diagonal of the square is 20 cm.

**Concept used: **

Perimter = 2√2 x diagonal

**Calculation: **

⇒ Perimeter = 2√2 x 20 = 40√2 cm

**∴ The diagonal of square is 20 cm, then perimeter of the square must be 40 √2 cm.**

- 963 m
^{2} - 639 m
^{2} - 936 m
^{2} - 693 m
^{2}

**Correct Answers Is: 3**

**SOLUTION**

Area of the rectangle = length × breadth

Length of the field = 90 m

Breath of the field = 60 m

⇒ Area of the field = 90 × 60 = 5400 m^{2}

Length of the field including path = 90 + 6 = 96 m

Breadth of the field including path = 60 + 6 = 66 m

⇒ Area of the field including path = 96 × 66 = 6336 m^{2}

∴ Area of the path = 6336 – 5400 = 936 m^{2}

- 42
- 36
- 45
- 33

**Correct Answers Is: 1**

**SOLUTION**

**Given:**

A wire is in the shape of a square of side 66 cm

**Formula Used:**

The perimeter of a Square = 4 × Side

The perimeter of a Circle = 2πr

**Calculation:**

According to the question,

Perimeter of Square = Perimeter of Circle

⇒ 4 × 66 = 2 × (22/7) × r

⇒ 2 × 3 = r/7

⇒ r = 42 cm

**∴ The radius of the circle is 42 cm.**

- 7√6
- 6√11
- 5√8
- 8√2

**Correct Answers Is: 2**

**SOLUTION**

**Given:**

The sides of a scalene triangle a = 8 cm, b = 5 cm, c = 9 cm

**Formula used:**

Using heron’s formula = √s × (s – a) × (s – b) × (s – c)

Where, S = semi – perimeter and a, b & c are the sides of the triangle

S = (a + b + c)/2

**Calculation:**

Here semi – perimeter (s) = (8 + 5 + 9)/2 = 11 cm

Using heron’s formula,

Area of the triangle = √s × (s – a) × (s – b) × (s – c)

⇒ √11 × (11 – 8) × (11 – 5) × (11 – 9)

⇒ √11 × 3 × 6 × 2

⇒ √396

⇒ 6√11 cm

**∴ The correct answer is 6√11 cm.**

- 12 cm.
- 13 cm.
- 14 cm.
- 15 cm.

**Correct Answers Is: 3**

**SOLUTION**

**Given:**

If the side of the square is increased by 5 cm, the area increased by 165 sq.cm.

**Formula Used:**

Area of square = Side^{2}

**Calculation:**

Let each side of the square be x.

⇒ (x+5)^{2} – x^{2} = 165

⇒ x^{2} + 25 +10x – x^{2} = 165

⇒ 10x +25 = 165

⇒ 10x = 140

⇒ x = 14.

**∴ The side of the square is 14 cm.**

- 1 : 4
- 4 : 1
- 2 : 1
- 1 : 2

**Correct Answers Is: 2**

**SOLUTION**

⇒ Base of triangle = b/2

Let the height of parallelogram be h_{1} and height of triangle be h_{2}

Given that the area of parallelogram is equal to area of triangle

⇒ 1/2 × b/2 × h_{2 }= b × h_{1}

_{2}∶ h

_{1 }= 4 ∶ 1

- 35 cm
- 30 cm
- 55 cm
- 33.5 cm

**Correct Answers Is: 1**

**SOLUTION**

**Given:**

The sides of a triangle are in the ratio 4 : 9 : 7

The sum of the shortest and the longest sides is 65 cm.

**Calculation:**

Shortest side of the triangle = 4 units

Longest side of the triangle = 9 units

The sum of the shortest and the longest sides = 4 + 9

⇒ 13 units

According to the question,

13 units = 65 cm

So, 1 unit = 5 cm

Length of the third side = 7 × 5

⇒ 35 cm

**∴ The required answer is 35 cm.**

^{2}, find the length of the base of the triangle.

- 12 cm
- 9 cm
- 18 cm
- 27 cm

**Correct Answers Is: 3**

**SOLUTION**

**Given:**

The length of the base of a triangle is 6 cm more than the corresponding altitude.

Area of the triangle = 108 cm2

**Concept used:**

Area of a triangle = 1/2 × b × h

b = base

h = height or altitude

**Calculation:**

Let the altitude be H cm

So, base = (H + 6) cm

According to the question,

1/2 × H × (H + 6) = 108

⇒ H^{2} + 6H – 216 = 0

⇒ H2 + 18H – 12H – 216 = 0

⇒ H(H + 18) – 12(H + 18) = 0

⇒ (H + 18)(H – 12) = 0

H = – 18, 12

Length cannot be negative so H = 12

So, base = 12 + 6 = 18 cm

**∴ The length of the base of the triangle is 18 cm**

^{2}and the ratio of the base and the height is 4 ∶ 5, then find its height.

- 25 m
- 20 m
- 30 m
- 24 m

**Correct Answers Is: 1**

**SOLUTION**

**Given:**

Area of a triangle = 250 m^{2}

Base : Height = 4 : 5

**Formula used:**

Area of a triangle = (1/2) × base × height

**Calculation:**

Let the base be 4x

Then height = 5x

Area of a triangle = 250 m2

⇒ (1/2) × 4x × 5x = 250

⇒ 10x^{2} = 250

⇒ x = 5

Height = 5x = **25 m**

10. A rectangular filed had length 32 cm and breadth 20 cm. How many square tiles of 4 cm should be used to cover the rectangular field?

- 40
- 45
- 37
- 42

**Correct Answers Is: 1**

**SOLUTION**

**Given:**

Length of rectangular field = 32 cm

Breadth of rectangular field = 20 cm

Length of tile = 4 cm

**Formula Used:**

Area of square = side × side

Area of rectangle = length × breadth

**Calculations:**

Length of rectangular field = 32 cm

Breadth of rectangular field = 20 cm

Length of tile = 4 cm

⇒ Area of rectangular field = (32 × 20) = 640 cm^{2}

Area of each tile = (4 × 4) = 16 cm^{2}

⇒ Number of tiles = (640/16) = 40

**∴ The number of square tiles used to cover the rectangular field is 40.**

- 40%
- 80%
- 96%
- 82%

**Correct Answers Is: 3**

^{2}. Find the cost of laying carpet on a triangular field having sides 10m, 20m & 20m.

- 900
- 250 √15
- 150 √15
- 350 √15

**Correct Answers Is: 2**

- 36√3 cm
^{2} - 38√3 cm2
- 34√3 cm2
- 40√3 cm2

**Correct Answers Is: 1**

**SOLUTION**

**Given:**

Side of equilateral triangle = 12 cm

**Formula used:**

Area = (1/4) × a^{2} × √3

**Calculations:**

According to the questions,

⇒ Area = (1/4) × (12)2 × √3

⇒ Area = (1/4) × 144 × √3

⇒ Area = 36 × √3 = 36√3 cm^{2}

**∴ The area of an equilateral triangle will be 36√3 cm2.**

^{2}. If its length is 18 cm, then what is its perimeter (in cm)?

- 62
- 68
- 64
- 66

**Correct Answers Is: 3**

**SOLUTION**

**Given:**

Area of a rectangle = 252 cm2

Length of the rectangle = 18 cm

**Concept used:**

Area of rectangle = Length x Breadth

Perimeter of rectangle = 2 x (Length + Breadth)

**Calculation:**

Let the breadth of the rectangle be b cm.

According to the question,

⇒ 252 = 18 x b

⇒ b = 252/18 = 14 cm

So, the breadth of the rectangle is 14 cm.

Now,

Perimeter of the rectangle

⇒ 2 x (18 + 14)

⇒ 2 x 32 = 64 cm

**∴ The perimeter of the rectangle is 64 cm.**

- 10 cm
^{2} - 8 cm
^{2} - 6 cm
^{2} - 4 cm
^{2}

**Correct Answers Is: 2**

**SOLUTION**

**Given:**

Diagonal = 4 cm

**Formula Used:**

Area = (side)^{2}

Diagonal = √2 × side

**Calculation:**

4 = √2 × side

⇒ side = 2√2 cm

∴ Area of the square = (2√2)^{2}= 8 cm

^{2}

^{2}. If the same wire is bent in the form of a circle, find the area of the circle. (Use π = 22/7)

- 154 cm
^{2} - 153 cm
^{2} - 155 cm
^{2} - 150 cm
^{2}

**Correct Answers Is: 1**

**SOLUTION**

^{2}

Let the side of square be ‘a’ cm,

⇒ a^{2 }= 121 cm^{2}

⇒ a = 11 cm

Now, the length of the wire = Perimeter of square

⇒ Length = 4 × 11 = 44 cm

Also, Length of wire = Perimeter of circle

⇒ 2πr = 44 cm

⇒ 2 × 22/7 × r = 44 cm

⇒ r = 7 cm

Area of circle = πr^{2}

^{2}

- 55 mtr
- 110 mtr
- 220 mtr
- 230 mtr

**Correct Answers Is: 3**

**SOLUTION**

**Given:**

The ratio of outer and inner perimeters of a circular path = 23 ∶ 22

The path is 5 m wide.

**Concept used:**

Circumference of circle = 2πr

Diameter = 2 × Radius

**Calculation:**

- 10 ∶ 1
- 5 ∶ 1
- 22 ∶ 7
- 50 ∶ 1

**Correct Answers Is: 1**

**SOLUTION**

**Given:**

The area of one circle is 100 times the area of another circle.

**Formula used:**

Area of Circle = πr^{2}

Circumference of circle = 2πr

r = radius

**Calculations:**

Let the radius of the circles be r_{1} and r_{2}

According to the question,

π(r_{1})^{2} = 100 × π(r_{1})^{2}

⇒ (r_{1}/r_{2})² = (100)

⇒ r_{1}/r_{2} = 10

Ratio of their circumferences = 2πr_{1}/2πr_{2} = r_{1}/r_{2} = 10

**Hence, The Required ratio is 10.**

- 400 m
^{2} - 450 m
^{2} - 350 m
^{2} - 250 m
^{2}

**Correct Answers Is: 3**

**SOLUTION**

**Given:**

Length of park = 40 m

Breadth = 25 m

A 2.5 m wide path is constructed outside the park

**Formula Used:**

Area of park = l x b

**Calculations:**

According to the formula,

Area of park = l x b = 40 x 25 = 1000 m^{2}

Area of park with a path will be

⇒ Length changes to = 40 + 2.5 + 2.5 = 45 m

⇒ Breadth changes to = 25 + 2.5 + 2.5 = 30 m

⇒ Area of park with path = 45 x 30 = 1350 m^{2}

So, the Area of the path will be

Area of path = Area of the park with path – Area of park

⇒ 1350 – 1000 = 350 m^{2}

**∴ The area of the path is 350 m ^{2}**

- 1 ∶ 2
- 1 ∶ 3
- 1 ∶ √2
- 1 ∶ 4

**Correct Answers Is: 1**

**SOLUTION**

**Formula used:**

Area of circle = πr^{2}

Area of square = (side)^{2}

**Calculation:**

Let the radius of smaller and larger circles be r and R respectively and the sides of smaller and larger squares be a and A respectively.

Area of smaller circle = πr^{2} = 1

⇒ r^{ }= 1/√π

Circumference of smaller circle = Circumference of smaller square

⇒ 2πr = 4a

⇒ a = √π/2

Area of smaller square

⇒ a^{2} = π/4 ———-(1)

Area of larger circle = πR^{2} = 2

⇒ R = √2/√π

Circumference of larger circle = Circumference of larger square

⇒ 2πR = 4A

⇒ A =

Area of larger square

⇒ A^{2} = 2π/4 = π/2 ———-(2)

from equation (1) & (2)

⇒

**∴ The correct answer is 1 : 2.**

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