Area

Area of a square = 1/2 (diagonal) 2

                = 1/2 (40)2

                = 1/2 * 1600

                = 800 sq. m.

Let the length of the rectangle be 'x' and breadth of the rectangle be 'y'

According to the question:

2(x + y) - x = 100

2x + 2y - x = 100

x + 2y = 100

From this we cannot find 'y' (breadth), so the given data is inadequate.

When d1 and d2 are the diagonals of rhombus then,
The Side of rhombus = Area Aptitude

Area Aptitude

Squaring both sides

202 = 16^2 + d2^2

400 = 256 + d2^2

d2^2 = 400 - 256

d2 = √144

d2 = 12

Area of rhombus =1/2( d1 × d2 )

 =1/2 ( 16 × 12 )=96 cm^2

Area of the entire grass field including the path = Length (85 + 5 +5) * Breadth (65 + 5+5)
                                                                            = 95 * 75 = 7125 sq. m.

Area of the grass field excluding the path = 85 * 65 = 5525 sq. m.

So, area of the path = 7125 - 5525 = 1600 sq. m.

The cost of constructing is Rs. 5 per square meter.

So, the cost of constructing the entire path = 1600 * 5 = Rs. 8000

Length of the hall = 20 m,

Breadth of hall = 15 m,

Area of hall = L x B = 20 x 15 = 300 m2

Length of hall with verandah = 20 + 2.5 + 2.5 = 25 m,

Breadth of hall with verandah = 15 + 2.5 + 2.5 = 20 m,

Area of hall with verandah = 25 x 20 = 500 m2

Area of verandah = area of hall with verandah - area of hall

= 500 - 300 = 200 m2

Cost of flooring the verandah is Rs. 3.50 per square meter.

So, the cost of flooring the entire verandah = 3.50 * 200 = Rs. 700

Let the breath = x

So, the Length = 3x

Perimeter of a rectangle = 2 (Length + Breadth)
So, 2 (3x + x) = 106
      6x + 2x = 106
      8x = 106
       x = 104/8 = 13

Now, Breadth = 13, so, length = 13 * 3 = 39

So, its area = Length * Breadth
                     = 39 * 13 = 507 sq. m.

Let breadth = X meters. Then, length = (X+ 40) meters.
Perimeter = 10600/53 =200 m
∴ 2[(X + 40) + X] = 200  2X + 40 = 100  2X = 120
⇒X = 60.
Hence, length = x + 40 = 100 m.

Parallel sides of a trapezium = 6 cm, and 10 cm
Area of trapezium = 1/2( sum of the parallel sides ) × distance between the parallel sides

32= 1/2( 6+10 ) × distance
32=8 × distance

Distance = 32/8 = 4 cm

So, the distance between the parallel lines of trapezium = 4 cm.

The ratio between the new area and the original area of the square can be found by using the formula for the area of a square and the percentage increase in the side length.

The original area of the square is s^2, where s is the side length. After the side length is increased by 50%, the new side length is 1.5s.

The new area of the square is (1.5s)^2 = 2.25s^2.

To find the ratio between the new area and the original area, we divide the new area by the original area: 2.25s^2 / s^2 = 2.25.

Therefore, the ratio between the new area and the original area of the square can be represented as 2.25 : 1 which means for every 1 unit of original area, the new area is 2.25 unit.

Ratio between the sides of rectangle = 3: 4

   Let the ratio constant be x then,

   Length = 3x and breadth = 4x

   Area = L x B

              7500=3x × 4x=12x^2
              7500/12= x^2=625

                x=25

Length = 3 x 25 = 75 m, and Breadth = 4 x 25 = 100 m

Perimeter = 2(75 + 100) = 2 x 175 = 350 m

Cost of fencing 1 meter = 25 paise

Cost of fencing 350 m = 350 x 25 = 8750 paise

In rupees: Rs. 87.50

Triangle area = 12 * base * height
As a result, the area is 12 * 5 * 10 = 25 square metres.

 
The area of a right angled triangle = ½ * base * height

Base = 10, Hypotenuse = 20

Height2 = Hypotenuse2 - Base2 
          = 202 - 162
          = 400 - 256
Height2  = 144
Height  = 12

Area = ½ * base * height
           = ½ * 10 * 12
          = 60 meters

 
Let the sides are 10x, 24x, and 26x.
The perimeter is 300 m.
So, 10x + 24x + 26x = 300
60x = 300
x= 5

So, the sides are 10 *5 = 50 meters
24 * 5 = 100 meters
26 * 5 = 130 meters
102 + 242 = 262 so, it is a right triangle.
       100 + 576 = 676

The area of a right triangle is = 1/2 * base * height
              = 1/2 * 50 * 100
              = 2500 m2 
 

One round of the park is equal to the perimeter of the park.

So, by completing one round, the cat covers a distance equal to the perimeter of the park.

Now, Distance or perimeter = speed * time
                                            = 18 * (10/60)
                                            = 3 km or 3000 meters

Let Length = 4x and breadth = 2x

So, Perimeter: 2 (4x + 2x) = 3000
8x + 4x = 3000
12x = 3000
x= 3000/12= 250 meters

So, Length = 4 * 250 = 1000 meters

And, Breadth = 2 * 250 = 500 meters

Area = Length * Breadth
      = 1000 * 500
      = 50000 sq. m.

Let the length of the rectangle be 5x, and breadth be 3x,
Perimeter of a rectangle = 2(l +b) = 480
                                         2(5x + 3x) = 480
                                         2 x 8x = 480
                                         16x = 480
                                         x = 480/16 = 30

∴ Length = 5 x 30 = 150 m
                  Breadth = 3 x 30 = 90 m

And, Area of rectangle = L x B
                                     = 150 x 90 = 13500 m2 

Perimeter of Square = 4 x side
4 x side = 24
Side = 24/4 = 6 cm
One of the sides of the square is 6 cm.

 
Area of a square:
side2 = Area Aptitude × (diagonal)2 

                         = Area Aptitude x 162 

                         = Area Aptitude x 256

                         = 128 m2 
 

 
Side of Square = 5 cm, and 
length of one side of rectangle = 5/2 = 2.5 cm

Let the length of the other side of the rectangle = B

As per the question:

Area of rectangle = Area of square

Length x Breadth = Side x Side
                2.5 * B = 5 * 5
                         B = 25/2.5
                         B = 10 cm

 
Perimeter of a rectangle = 2 (Length + Breadth)

Let length is L and breadth is B.

So, as per the question = 2(L+B)/B = 10/2
                                     2(L+B)/B = 5/1
                                     2L + 2B = 5B
                                     2B - 5B = - 2L
                                     - 3B = - 2L
                                     B = 2/3 L

Given Area = 430 sq. cm.

Area = Length * Breadth
         430 = L * 2/3 L
         430 = 2/3 L2

Or L2 = 1290 / 2
  L2 = 645
   L = 25.4 cm
 

 
By pythogerous theorem Other side = √((34)^2- (30)^2) = 16
⇒Area = (30 x 16) m^2 = 480 m2
 

Let length = X and breadth = Y. Then,
2 (X + Y) = 92 OR X + Y = 46 AND X^2 + Y^2 = (34)^2 = 1156.
Now, (X + Y)^2 = (46)^2
⇔ (X2 + Y2) + 2XY = 2116 ⇔ 1156 + 2XY = 2116
⇒ XY=480
∴ Area = XY = 480 cm2

Let breadth = X. Then, length = 3X.
Then,	(3X - 9) (X + 9) = 3X * X + 81
⇒3X2+27X-9X-81=3X2+81
18X=162
⇒X=9 cm
∴ Length of the rectangle = 9 cm

 
Area of the square = 1/2 (diagonal)^2= 1/2x7.2^2≡
 7.2x7.2/2=25.92 m2
 

Let the diagonals of the squares be 3X and 7X respectively.
Ratio of their areas = (1/2)*(3X)2 :( 1/2)*(7X)2 = 9X2: 49X2 = 9: 49.

Side of first square = (80/4) = 20 cm;
Side of second square = (64/4)cm = 16 cm.
Area of third square = [(20)^2 - (16)^2] cm^2
= (400 - 256) cm^2 = 144 cm^2.
Side of third square = √144 cm = 12 cm.
Required perimeter = (12 x 4) cm = 48 cm.

Length of largest tile = H.C.F. of 3034 cm and 1804 cm = 82 cm.
Area of each tile = (82 x 82) cm^2.
Required number of tiles  3034x1804/82x82  = 37x22=814.

Let each side of the square be X. Then, area = X^2.
New side =(116X/100) =(29X/25). New area = (29X/25)^2
Increase in area = (29X/25)^2 - X^2 =841/625X^2 - X^2=216/625X^2
⇒ Increase% = [(216/625X^2x1/(X^2))*100] % = 34.56%.