- The perimeter of an equilateral triangle is equal to the perimeter of a square whose diagonal is 9√2 cm. Find out the area of the equilateral triangle ?
48√360√330√336√320√3Option D

side of square=9√2/√2=9

let the side of equilateral triangle be x cm.

3x=4*9

x=12

area of equilateral triangle= √3/4*12*12=36√3 - If ratio of height and radius of a cone is 5:6. Volume of cone is 480π cm^3, then find slant height of cone (in cm) ?
2√614√618√509√6810√52Option A

let height and radius of cone be 5x and 6x.

volume of cone =480π

1/3*π*6x^2*5x=480π

x^3=8

x=2 cm

height=10cm , radius=12 cm

so, slant height of cone =√(r^2+h^2)

= √(144+100)=√244=2√61 - Circumference of a circle A is 2 times perimeter of a square. Area of the square is 484 cm^2. What is the area of another circle B whose radius is half the radius of the circle A ?
530640590616none of theseOption D

Area of the square =484cm

side of square =22cm.

perimeter of square =22*4=88cm.

ATQ,

circumference of a circle A=88*2 =176cm.

2πr =176

r=176*7/44 =28

Radius of circle B= 28/2 =14cm.

Area of circle B=22/7*14*14 =616cm^2 - If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 288 m^2 . What is the area of the original rectangle ?
400300520220none of theseOption B

Percentage change in area =

+20-20-(20*20)/100 =-4%

96%= 288

100%=288/96*100= 300 m^2 - Side of a rhombus is 20cm and the ratio of diagonals of a rhombus is 3:4, then find the area of the rhombus .
384264544288484Option A

Side of rhombus =20cm.

Let,

two diagonals of a rhombus be 3x and 4x.

side =√(3x)^2+(4x)^2

= 9x^2+16x^2 =5x

5x=20

x=4

two diagonals =(4*3*2) and (4*4*2) =24 and 32

Area =1/2*24*32 =384 cm^2. - The side of a square is 20% more than the side of an equilateral triangle whose perimeter is 75m. Find the ratio between perimeter of square to area of triangle.
96:125√348:55√332:5896:130√332:42Option A

perimeter of triangle=75

side of triangle=75/3=25m

side of square=25*120/100=30 m

perimeter of square=4*30=120 m

area of triangle=√3/4*25*25=625√3/4 m^2

ratio=120:625√3/4=480:625√3=96:125√3 - Radius of circular field is 40% more than length of a rectangular field, having the area 80 m^2. If circumference of a circle is 88m, then radius of circular field is what percent more than breadth of rectangular field ?
605012075100Option D

let radius of circle =7x

and length of rectangular field=10m

area of rectangular field=80 m^2

10*breadth=80

breadth=8m

required percentage=14-8?8*100=6/8*100=75% - Perimeter of a circle is 88cm. Find volume of a cylindrical vessel whose radius is equal to the radius of circle and height of cylindrical vessel is 20 cm.
1500012320142201678020400Option B

Perimeter of circle =88

r=88*7/44=14 cm

radius of cylindrical vessel =22/7*14*14*20 = 12320 cm^2 - The ratio between length and breadth of a rectangular field is 5:4 . If area of rectangular field is 320 m^2, then find the perimeter of rectangular field.
64401007284Option D

Let length of field =5x

breadth of field =4x

ATQ,

5x*4x =320

20x^2=320

x^2 =320/20 =16

x=4

Perimeter =2(5x+4x) =18x =18*4= 72 - The total area of a circle and a square is equal to 1241 cm^2. The diameter of the circle is 28cm. What is the sum of the circumference of the circle and the perimeter of the square ?
132188192288196Option B

diameter of circle=28cm

radius=14cm

area of circle=22/7*14*14=616

ATQ,πr^2+a^2=1241

a^2=1241-616=625

a=25

circumference of the circle=2*22/7*14=88

perimeter of square=4a=4*25=100

sum=88+100=188

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