[Anagha Babu]

Given the length, width and thickness of the metal sheet (cuboid)<div>

The volume of cuboid= length ×width× thickness

V=27cm×8cm×1cm

= 216cm

Since the metal sheet is melted into a cube , we can say that

Volume of cuboid= volume of cube

Volume of cube= a^3

( Where a is the side of the cube)

216cm= a^3

6cm=a

Therefore the side’s of the cube will be 6cm

</div>

[Anagha Babu]

Assume that b < d i.e b-d <0 ….(1)

Given that a <c i.e a-c < 0and a+b=c+d

The given equation can be written as

a-c=d-b

We know that a-c <0

Therefore d-b <0 …..(2)

Equation (2) contradicts our assumption

Which implies that our assumption has gone wrong

Therefore d <b

[Anagha Babu]

Let x be a odd number.

Let x-2,x,x+2 be the three odd consecutive numbers corresponding to x .

Given that the sum of three odd consecutive numbers is equal to 27

That is ,

(x-2)+x+(x+2) =27

3x=27

x=9

Therefore the three odd consecutive numbers are 7,9,11

[Anagha Babu]

Given that the area of the circle= the perimeter of the circle.

Let ‘r’ be the radius of the circle

Area of the circle=πr^2

Perimeter of the circle=2πr

On equating both the equation we get

πr^2=2πr

πr^2 – 2πr =0

πr(r-2)=0

π is never equals to 0 , therefore either r=0 or r-2=0

r cannot be equal to 0 because if r=0 a circle cannot be formed .

Therefore, r-2=0

That is , r=2

Hence we can conclude that, if area and perimeter of a circle are equal then it’s radius will be 2units.

[Anagha Babu]

The garden is in the form of a rectangle whose length is given as 12m and width is 8m

1) Perimeter of the rectangle= 2(l+b)

= 2(12+8)

= 40m

2) area of the rectangle = l×b

=12×8

=96m

• This reply was modified 1 year, 10 months ago by  Anagha Babu. Reason: Some notation came in between the sentences after posting

[Anagha Babu]

Quadrilateral is a figure with for angles and sum of its angles equals 360 degree

In the above question the angels are given in the ratio form . Therefore let us choose the four angles as 1y , 2y, 3y, 4y ( same as the ratio given)

y is a random variable.

1y+2y+3y+4y =360 ( sum angle property)

10y=360

y=360÷10

y=36

Therefore the measure of four angles are 1×36,2×36, 3×36, 4×36

Which is the same as

36°, 72°,108°,144°

[Anagha Babu]

Given: (1) perimeter of the square= perimeter of the rectangle

(2) length of the rectangle is 80cm

(3) side of the square is 60cm

Answer:

Let us denote the side of the square as ‘a’

Perimeter of the square= 4×a (formula)

Given that a=60cm ……..(3)

Therefore perimeter of the square=4×60

So perimeter=240cm

Perimeter of the rectangle=2(l+b)

Where ‘l’ denote length and ‘b’ denote breadth or width

Since it is given that the square and rectangle have same perimeter we can equate them .

That is ,

2(l+b)=240cm

Given that the length of the rectangle is 80cm

Therefore,

2(80+b)=240

80+b=240÷2

80+b=120

b=120-80

b=40

Area of the rectangle= l×b

We know that

l=80 and b=40

Therefore,

Area of the rectangle= 80×40=3200cm