Area- Aptitude Questions and Answers - in Hindi

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

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

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

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°

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.

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

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.

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

Let x and y be the length and breadth respectively.
Area of rectangle = x*y
Area of square = (x-4) * (y+3)

As is given , (x-4) * (y+3)= x*y
3x – 4y = 12 ……………………………….(i)

for a square, length = width
(x-4) = (y+3)
x - y = 7 ……………………………….(ii)

Solving eq (i) & (ii) x= 16 and y = 9
Therefore perimeter of rectangle = 2(x+y)= 2(16+9)= 50 cm

Let the side of squares be x and y respectively. Then
As is given ,
x² / y² = 225/256
x / y = √(225/256) = 15 / 16

Ratio of their perimeters = 4x / 4y = x / y = 15 / 16

Given that circumference of semi circle is = 180
let the radius of this Semi circle be R
πR + 2R = 180
R(22/7 + 2)= 180
So, R =180*7 /36

Diameter of this semi circle, D = 2*R

Now, Side of the square = 160/100 D = 160/100 * 2R = 3.2*R

Perimeter of square = 4 * Side of the square = 4*3.2*R = 448

If a, b, c represents the sides of the triangle, then sum of the two sides must be greater than the third
side.
Since, 2 + 3 < 6
Hence, (2, 3, 6) can’t be side of a triangle.

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

Since the angles of a triangle are in the ratio 2 : 4 : 3.

Smallest angle = (2/ 2+4+3)180°
= (2/9)180°
= 40°

Area of a square = 1225 m²
(side)² = 1225
side = √1225 = 35 m

Now, perimeter of a square = 4*side = 4*35
=140 m

Area of a square = 7396 m²
(side)² = 7396
side = √7396 = 86 m

Now, perimeter of square = 4*side = 4*86
=344 m