MCQ: Area and Perimeter- 3 - SSC CGL MCQ

# MCQ: Area and Perimeter- 3 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Area and Perimeter- 3

MCQ: Area and Perimeter- 3 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Area and Perimeter- 3 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Area and Perimeter- 3 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Area and Perimeter- 3 below.
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MCQ: Area and Perimeter- 3 - Question 1

### The radius of a circle is increased so that its circumference increase by 5%. The area of the circle will increase by ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 1

Let circumference = 100 cm .
Then, ∵ 2πr = 100
⇒ r = 100/2π
=50/π
⇒ New circumference
= 105 cm
Then, 2πR = 105
⇒ R = 105 / (2π)
&rArr Original area = [ π x (50/π) x (50/π) ]
= 2500/π cm2
⇒ New Area = [π x (105/2π) x (105/2π)]
= 11025 / (4π) cm2
⇒ Increase in area = [11025/(4π)] - 2500/π cm2
= 1025 / 4π cm2
Required increase percent [1025/(4π)] x 2500/π x 100 = 41/4%
= 10.25%

MCQ: Area and Perimeter- 3 - Question 2

### The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 2

∵ 22/7 x r2 = 462
⇒ r2 = (462 x 7) /22 = 147
⇒ r = 7√3 cm
∴ Height of the triangle = 3r = 21√3 cm
Now, ∵ a2 = a2/4 + (3r)2
⇒ 3a2/4 = (21√3)2
⇒ a2 = (1323 x 4)/3
⇒ a = 21x 2 = 42 cm
∴ Perimeter = 3a = 3 x 42
=126 cm

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MCQ: Area and Perimeter- 3 - Question 3

### A room 5.44 m x 3.75 m is to be paved with square tiles. the least number of tiles required to cover the floor is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 3

Area of the room =(544 x 374) cm2
size of largest square tile = H.C.F. of 544 & 374
= 34 cm
Area of 1 tile = (34 x 34) cm2
∴ Least number of tiles required
= (544 x 374) / (34 x 34) = 176

MCQ: Area and Perimeter- 3 - Question 4

A polygon has 44 diagonals the number of its sides is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 4

Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is nC2
These nC2 lines also include n sides of polygon.
Therefore, the number of diagonals formed is nC2 - n.
Thus, nC2 - n = 44
⇒ [n(n - 1)/2] - n = 44
⇒ ( n2 - 3n) / 2 = 44
⇒ n2 - 3n = 88
⇒ n2 - 3n - 88 = 0
⇒(n - 11) (n + 8) = 0
∴ n = 11

MCQ: Area and Perimeter- 3 - Question 5

If the area of an equilateral triangle is x and its perimeter is y, then which one of the following is correct ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 5

Area of equilateral triangle = √3a2/4 = x ......(i)
And perimeter = 3a = y
⇒ a = y/3 ....(ii)
Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
√3 (y/3)2/4 = x
⇒ x = √3 x y2/36
⇒ x = y2/3√3x = y2/12√3
12√3 x = y2
On squaring both sides, we get
y4 = 432x2

MCQ: Area and Perimeter- 3 - Question 6

The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 6

Given that, l = 2b [Here l = length and b = breadth]
Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm
According to the question,
(l - 5) (b + 5) = lb + 75
⇒ (2b - 5) (b + 5) = 2b2 + 75 [since l = 2b]
⇒ 5b - 25 = 75
⇒ 5b = 100
∴ b = 100/ 5 = 20
∴ l = 2b = 2 x 20 = 40 cm

MCQ: Area and Perimeter- 3 - Question 7

How many circular plates of diameter d be taken out of a square plate of side 2d with minimum loss of material ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 7

Area of square plate = (Side)2
= (2d)2
= 4d2
Area of circular plate = π (d/2)2
= πd2/4
∵ Number of square plates
= [(4d2)/4] / [(πd2)/4]
= (4 x 4)/π
≈ 5
Since, nearest integer value is 5.

MCQ: Area and Perimeter- 3 - Question 8

The altitude of an equilateral triangle of side 2 √ 3 cm is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 8

∵ 1/2 x 2 √ x h
= √3/4 x (2 √3)2
∴ h = 3 cm.

MCQ: Area and Perimeter- 3 - Question 9

The length of minute hand of a wall clock is 7 cms. The area swept by minute hand in 30 minutes is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 9

Angle swept in 30 min= 180°
Area swept = [(22/7) x 7 x 7] x [180°/360°] cm2
= 77 cm2

MCQ: Area and Perimeter- 3 - Question 10

A park is in the form of a square one of whose sides is 100 m . The area of the park excluding the circular lawn in the centre of the park is 8614 m2. The radius of the circular lawn is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 10

Area of park = 100 x 100 = 10000 m2
Area of circular lawn = Area of park - area of park excluding circular lawn
= 10000 - 8614
= 1386
Now again area of circular lawn = (22/7) x r2 = 1386 m2
⇒ r2 = (1386 x 7) / 22
= 63 x 7
= 3 x 3 x 7 x 7
∴ r = 21 m

MCQ: Area and Perimeter- 3 - Question 11

The ratio of the corresponding sides of two similar triangles is 3 : 4, The ratio of their areas is ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 11

Ratio of similar triangle
= Ratio of the square of corresponding sides
= (3x)2 / (4x)2 = 9x2 / 16x2
= 9/16 = 9 : 16

MCQ: Area and Perimeter- 3 - Question 12

A square, a circle and equilateral triangle have same perimeter.
Consider the following statements.
I. The area of square is greater than the area of the triangle.
II. The area of circle is less then the area of triangle.
Which of the statement is/are correct ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 12

Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2πr = 4a
⇒ a = πr/2
∴ Area of square = (πr/2)2 = π2 /4r2 = 9.86r2/4 = 2.46r2
and area of circle = πr2 = 3.14;r2
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2πr
⇒ x = 2πr/3
∴ Area of equilateral triangle = √3/4 x 2
= √3/4 x 4π2r2/9
= π2/3√3r2
= 1.89r2
Hence, Area of circle > Area of square > Area of equilateral triangle.

MCQ: Area and Perimeter- 3 - Question 13

The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 13

We know that, the radius of a circle inscribed in a equilateral triangle = a/[2√3]
Where, a be the length of the side of an equilateral triangle.
Given that, area of a circle inscribed in an equilateral tringle = 154 cm2
∴ π(a/2√3)2 = 154
⇒ (a/2√3)2 = 154 x (7/22) = (7)a2
⇒ a = 42√3 cm
Perimeter of an equilateral triangle = 3a
= 3(14√3)
= 42√3 cm

MCQ: Area and Perimeter- 3 - Question 14

The area of rectangle is 1.8 times the area of a square. The length of the rectangle is 5 times the breadth. The side of the square is 20 cm. What is the perimeter of the rectangle ?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 14

Area of square = (Side)2 = 202
= 400 sq cm
∴ Area of rectangle
= 1.8 x 400 = 720 sq cm
Let length and breadth of rectangle be 5k and k respectively.
Then, according to the question,
5k x k = 720
⇒ 5k2 = 720
⇒ k2 = 720/5 = 144
∴ k = √144 = 12 cm
Perimeter of rectangle = 2(5k + k) = 12k
= 12 x12 = 144 cm

MCQ: Area and Perimeter- 3 - Question 15

One diagonal of a rhombus is 60% of the other diagonal. Then, area of the rhombus is how many times the square of the length of the larger diagonal?

Detailed Solution for MCQ: Area and Perimeter- 3 - Question 15

Let one diagonal be k.
Then, other diagonal = (60k/100) = 3k/5 cm
Area of rhombus =(1/2) x k x (3k/5) = (3/10)
= 3/10 (square of longer diagonal)
Hence, area of rhombus is 3/10 times.

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