Area- Aptitude Questions and Answers

View in English View in Hindi

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is?

A)

6 cm


B)

5 cmm


C)

4.5 cm


D)

4 cm



Correct Answer :

4 cm


Explanation :

Let l and b the length and breadth of the rectangle respectively.
Now, according to the question 2(l + b) = 10
l + b = 5 …eq(i)
and lb = 4 …eq(ii)
From Eqs. (i) and (ii), we have
l(5 - l) = 4
5l - l2 = 4
l2 - 5l + 4 = 0
(l - 4)(l - 1) = 0

length, l = 4 or 1

Post comment
Cancel
Thanks for your comment.!
Write a comment(Click here) ...
View in English View in Hindi

There is a path made around a circular park. If the difference of external and internal perimeters is 132 meter, then the width of the path is:

A)
22 m

B)
20 m

C)
21 m

D)
24 m


Correct Answer :

21 m


Explanation :

Let the inner and outer radii be r and R meters.
then width of the path => 2(pi)R-2(pi)r = 132m
there pi =22/7
So R-r= 132*7/2*22 =21m

therefore width of the path is R-r=21m

The base of right-angled triangle is 5 meters and hypotenuse is 13 meters . Its area will be ?

A)
25 m2

B)
28 m2

C)
30 m2

D)
24 m2


Correct Answer :

30 m2


Explanation :

Hypotenuse = √(base2+height2)
height2 = Hypotenuse2 - base2
height = √(132 - 52)
⇒ √144 ⇒ 12

Area of the triangle = 1/2(base*height)
=1/2(5 * 12 ) m2
= 30m2

If the side of a square is increased by 25%, then how much percent does its area get increased ?

125
156.25
50
56.25

Correct Answer :

56.25


Explanation :

Let side of square is 100 m2 Then, side = 10 m
And, Area = length of a side2 (10)2 m2

increased side by 25 Then, new side = 125 % of 10 ⇒ (125/100) x 10 ⇒ 12.5 m
And,new area = length of a side2 ⇒ (12.5)2 sq. m

Increase in area = (12.5)2 - (10)2 m2
= 156.25 - 100 m2
= 56.25 m2
% Increase = 56.25

if the side of a square be increased by 4 cms. The area increased by 60 sq. cms . The side of the square is ?

12 cm
13 cm
14 cm
5.5 cm

Correct Answer :

5.5 cm


Explanation :

Let each side = x cm
Then, (x + 4 )2 - x2 = 60
⇒ x 2 + 8x + 16 - x2 = 60
⇒ x = 5.5 cm

If the diameters of a circle is increased by 100% . Its area is increased by ?

100%
200%
300%
400%

Correct Answer :

300%


Explanation :

Area of circle = πd2/4

diameters increased by 100%, then new area = π(2d)2 /4 => πd2
Then, New area = (πd2 - πd2/4) => 3πd2/4

increase percent =[(3πd2/4) / ( πd2/4) ]*100 %
= [(3πd2/4) x (4/πd2)]*100 %
= 300%

Find the area of a triangle whose sides measure 8 cm, 10 cm and 12 cm?

8√63 sq cm
5√63 sq cm
6√53 sq cm
7√93 sq cm

Correct Answer :

5√63 sq cm


Explanation :

Area of triangle = √[s(s-a)(s-b)(s-c)] there s = (a+b+c)/2

let, a = 8 cm, b = 10 cm and c = 12 cm
then,s = (a + b + c)/2
= (8 + 10 + 12)/2
= 15 cm

so,Area of triangle = √s(s - a) (s - b) (s - c)
= √[15 * (15 - 8) * (15 - 10) * (15 - 12)]
= √1575
= √[25 x 63]
= 5√63 cm

One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram?

12.56 cm2
14.56 cm2
16.76 cm2
22.56 cm2

Correct Answer :

16.76 cm2


Explanation :

Area of parallelogram = base x height
= 8.06 x 2.08 = 16.76 cm2

Find the area of a rectangle having 15m length and 8m breadth.

120 sq m
111 sq m
115 sq m
125 sq m

Correct Answer :

120 sq m


Explanation :

Area of Rectangle= Length x Breadth
= 15 x 8 = 120 sq m

The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is _______?

A)

4


B)

5


C)

6


D)

8



Correct Answer :

4


Explanation :

Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal.
4x + 8 = 6x
2x = 8
x = 4

The perimeters of two squares are 160cm and 164cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares(in cm).

A)
81

B)
60

C)
36

D)
9


Correct Answer :

36


Explanation :

Perimeter of Square = 4 * length of a side
Area of Square= length of a side2

The perimeters of two squares are 160cm and 164cm ,
So the side of first square = 160/4 = 40 cm
side of second square = 164/4 = 41 cm

Area of third squre = 412 - 402 = 81 sq cm
Then, side of third square = √81 = 9 cm

required perimeter = 4*9 = 36 cm

The sides of a triangle are in the ratio 3:4:5. The perimeter of the triangle is 24cm. The area (in cm2) of the triangle is:

A)
39

B)
26

C)
24

D)
32


Correct Answer :

24


Explanation :

Perimeter = (a+b+c) ,there a,b,c are the sides of a triangle
Area = 1/2(base*height) = √[s(s-a)(s-b)(s-c)] there s = (a+b+c)/2

let's the sides of triangle are 3 cm, 4 cm, and 5 cm in length , then
Perimeter = 3 cm + 4 cm + 5 cm =12 cm

So Area = √[s(s-a)(s-b)(s-c)] there s = (a+b+c)/2 = 12/2 =6
Area = √[6(6-3)(6-4)(6-5)] =√[6*3*2*1] =6

hence Area may be 6 or multiple of 6 that is 6, 12 , 24 ...because sides are given in ratio

In a rhombus of side 10 cm, one of diagonals is 16 cm long. The length of In a rhombus of side 10 cm, one of diagonals is 16 cm long. The length of the second diagonal is ?

A)
16 cm

B)
12 cm

C)
18 cm

D)
20 cm


Correct Answer :

12 cm


Explanation :

The diagonals meet in the middle at a right angle.
All sides of rhombus are equal i.e. 10cm
(Side)2=(half of one diagonal)2+(half of second diagonal)2
by using this formula
(10)2=(8)2+(half of second diagonal)2
(half of second diagonal)2 = 36
half of second diagonal=6
second diagonal=12cm

Latest Updates

General Knowledge of MP

Under the Madhya Pradesh Ladli Laxmi Yojana, the beneficiary is paid the total amount on attaining the age of ?

Indian Politics

Who appoints the Chairman and the Members of the Union Public Service Commission?

General Knowledge of World

Which country will host the 2022 Football World Cup?

Area

The angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is?

Which one of the following triples does not represent the sides of a triangle?

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is?

Height and Distance

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60º and 45º respectively. What is the height of the lower plane from the ground?

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30º and 45º respectively. What is the height of the tree?

Trigonometry

What is the value of sinx √( 1 /1+cosx + 1 /1-cosx ) ?

What is cos4 A - sin4 A / cos2 A - sin2 A equal to?

If 7sin2 x +3cos2 x = 4, 0 < x < 90º ,then what is the value of tan x?

If x = a cosθ + b sinθ and y = a sinθ - b cosθ then what is x2 + y2 equal to?

Average

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are?

In an asymmetrical distribution, of the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is?

Let a, b, c, d, e, f, g be consecutive even numbers and j, k, l, m, n be consecutive odd numbers. What is the average of all the numbers?

Alligation or Mixture

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

Simplification

The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the square of these two numbers?