Area- Aptitude Questions and Answers

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One diagonal and perimeter of a rhombus are 24 cm and 52 cm respectively. The area of rhombus will be?

A)
60 cm2

B)
120 cm2

C)
100 cm2

D)
30 cm2


Correct Answer :

120 cm2


Explanation :


Side of roumbus =52/4 = 13 cm

Area of the roumbus = (product of diagonals)/2

Let ABCD is rhombus, in which Side of roumbus =AB=13cm , BD=24cm and AC=? cm
the digonal of rhoumbus bisect each other at right angle

in the right angel AOB
OA2+OB2=AB2
OA2+(BD/2)2=AB2
OA2+(12)2=(13)2
OA2= (13)2 - (12)2
OA = √(169-144) =√25 = 5
Hence the lenght of other dignoal is AC=2*OA= 2*5= 10cm
Thus,Area of the roumbus = (product of diagonals)/2
=> ( 24 * 10 ) /2 => 120 cm2

ABCD is a square of side X cm. Its side is increased by 30%. What is the change in its area?

A)
60%

B)
62.5%

C)
63%

D)
69%


Correct Answer :

69%


Explanation :

Let side = X cm
then Area = length of a side2 ⇒ (X)2 cm2

increased side by 30 then, new side = 130 % of X ⇒ (130/100) *X ⇒ 1.3X cm
And,new area = length of a side2 ⇒ (1.3)2 sq. cm

Increase in area = (1.3*X)2 - (X)2 cm2
= 1.69*X2 - X2
= .69*X2
% Increase = 69

The sides of a triangle a, b, c are such that 2a = 3b = 4c and its perimeter is 208 cm. What is the length of the longest side?

A)
48cm

B)
96cm

C)
64cm

D)
54cm


Correct Answer :

96cm


Explanation :

Let 2a = 3b = 4c = x
So, a = x/2 b = x/3 c = x/4
The L.C.M of 2, 3 and 4 is 12
Therefore, a : b : c = x/2 × 12 : x/3 × 12 : x/4 = 12
= 6x : 4x : 3x
= 6 : 4 : 3
Therefore, a : b : c = 6 : 4 : 3

the perimeter of a triangle is sum of its side
Lets take a variable x for the sides,
hence the sides will be 6x,4x,3x respectively.

Perimeter = 6x+4x+3x
208 = 6x+4x+3x = 13x
13x = 208
=> x = 208/13
x=16

Length of the longest side = 6x = 6 x 16 = 96.

What is the longest side of a rectangle which has a perimeter of 70 units and an area of 276 square units?

A)
12 units

B)
18 units

C)
23 units

D)
36 units


Correct Answer :

23 units


Explanation :

let Length =L and Width=W

Perimeter = 2(L + W) = 70
L + W = 35
L = 35 - W

Area = WL = 276
W(35 - W) = 276
35W - W2 = 276
0 = W2 - 35W + 276
0 = (W - 23)(W - 12)
W = {12, 23}
L = {23, 12}

Therefore, the sides of the rectangle are 23 and 12
The longest side of the rectangle is 23 units.

The length and breadth of a rectangular hall are 40 m and 30 m respectively. What is the distance between two opposite corners of the hall?

A)
20 m

B)
35 m

C)
50 m

D)
40 m


Correct Answer :

50 m


Explanation :

Distance between two corners of hall
= √(Length2 + Breadth2)
= √(402 + 302) = √(1600 + 900) = 50 m

The area of the base of a rectangular tank is 6500 cm2 and volume of water contained in it is 2.6 m3. The depth of water (in metres) in the tank is

A)
2.5

B)
3

C)
4

D)
5.5


Correct Answer :

4


Explanation :

Let the depth of water be x m.Then
(6500/10000) * x = 2.6
x =(2.6*10000)/6500
= 4 m

The ratio of areas of two squares A and B are 4:25. If the side of the square A is 6m. Then, what is the measure of the side of square B?

A)
256m

B)
15m

C)
12m

D)
32m2


Correct Answer :

15m


Explanation :

area of square A= (6)²= 36 m²
let side of square B is x, So area of square B= x² m²

As given 36:x²:: 4:25
36/x² = 4/25
9/x² = 1/25
(3/x)²= (1/5)²
3/x = 1/5
x = 15 m
So side of square B has a length of 15 m

What is the measure of the base angle of an isosceles triangle, if its vertical angle is 70°?

A)
110°

B)
55°

C)
90°

D)
70°


Correct Answer :

55°


Explanation :

The sum of all the angles of a triangle must equal 180 degrees.
An isosceles triangle has two (Base) angles that are equal. The vertex angle is the odd one. So:

the measure of each base angle x.then
x + x + 70 = 180
2x = 180-70
x = 110/2
x = 55
The base angles measure 55°

If 'x' units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?

A)

X


B)


C)

2πX


D)

X2



Correct Answer :

2πX


Explanation :

Let the radius of the circle be r .
The circumference of the circle will therefore be 2 πr .

If the radius is increased by 'X' units, the new radius will be (r + X) .

The new circumference will be 2 π(r + X) = 2 πr + 2 πX
Hence, the circumference increases by 2 πX units.

The sides of a triangle are 30, 40 and 50 cm. Then this triangle is a?

A)

right-angled triangles


B)

acute-angled triangle


C)

obtuse-angled triangle


D)

equilateral triangle



Correct Answer :

right-angled triangles


Explanation :

As per Pythagoras Theorem, a triangle with a right angle (an angle of 90°) has a special relationship between the lengths of its three sides.
If the longest side (called the hypotenuse) is c and the other two sides (next to the right angle) are called a and b, then:
a2 + b2 = c2 Pythagoras' Theorem

Therefore, the triangles that follow this rule will be right angled triangles.

The triangle with sides 30, 40, 50 follows the Pythagorean theorem, so it is a right angle
302 + 402 = 900 + 1600 = 2500 = 502

Also 30, 40 and 50 are multiples of 3, 4, and 5 which is a well known "the 3-4-5 triangle"

3-4-5 triangle: there are some right-angled triangles, where all three sides are whole numbers called Pythagorean Triangles. And the three whole number side-lengths are called a Pythagorean triple or triad.

Below the list examples of Pythagorean triples-
3, 4, 5
5, 12, 13
6, 8, 10
7, 24, 25
8, 15, 17
9, 12, 15
9, 40, 41
10, 24, 26
12, 16, 20
12, 35, 37
14, 48, 50
15, 20, 25
15, 36, 39
16, 30, 34
18, 24, 30
20, 21, 29
21, 28, 35
24, 32, 40
27, 36, 45
30, 40, 50

A polygon has 44 diagonals, the number of its sides are?

A)

9


B)

10


C)

11


D)

12



Correct Answer :

11


Explanation :

Polygon: A polygon is a 2-dimensional shape that is formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons.

Let the side is n. because there are n sides, we have to subtract n from total number of line formed by joining two adjacent vertices of polygon.

number of diagonals = nC2 -n = n(n-1)/2 - n
number of diagonals = n(n-3) / 2 = 44
n2 - 3n - 88 = 0
(n+3) (n-11) = 0

n=11 (n can not be negative)
So the number of sides in a shape with 44 diagonals is 11.

If the length and breadth of a rectangular plot were increased by 20 percent; then what would be the percent increase in the area of the plot?

A)

20%


B)

44%


C)

26%


D)

36%



Correct Answer :

44%


Explanation :

Let the length of rectangle be x and breadth be y
So Area= length*breadth= x*y

According to The question
length = x + x*20/100= x *(1 + 1/5)=6x/5
breadth = y + y*20/100=y *(1 + 1/5)= 6y/5

New Area= 6x/5 × 6y/5 = 36*xy/25

Changes in area= 36*xy/25 - xy =xy* (36-25 / 25) =11*xy/25

% change = (11*xy / 25)*100 / xy = 44% area would be increase

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