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If the ratio of areas of two squares is 289:121, then the ratio of their perimeters is

A.

11:17

B.

17:11

C.

2:1

D.

18:11

Answer with explanation

Answer: Option BExplanation

Let the side of the squares for the first and second square be ‘a’ & ‘b’ respectively

a^{2}/b^{2} = 289/121 = 17^{2}/11^{2}

Therefore, a/b = 17/11

Ratio of perimeters = 4a/4b

= (4 * 17)/(4 * 11)

= 17 : 11

Workspace

If one angle of a triangle is equal to half the sum of the other two equal angles, then the triangle is

A.

isosceles

B.

scalene

C.

equilateral

D.

right angled

Answer with explanation

Answer: Option CExplanation

Let first angle be x and other two equal angle be y.

Then from the question

x = (y + y)/2 = y

That mean x = y

So, x + x + x = 180^{0}

Or, 3x = 180^{0}

Or, x = 60^{0}

Hence, ∆ is equilateral triangle.

Workspace

The point equidistant from the vertices of a triangle is called its

A.

incentre

B.

circumcentre

C.

orthocentre

D.

centroid

Answer with explanation

Answer: Option BExplanation

The circumcenter of a triangle is the point that is at an equidistance from the vertices of the triangle. In the following triangle, D is the circumcenter of the triangle and therefore are AD = BD = CD

Workspace

The diagonal of a cube is √192 cm. Its volume (in cm3) will be

A.

216

B.

432

C.

512

D.

624

Answer with explanation

Answer: Option CExplanation

Let a be the length of side of cube.

The length of the diagonal of the cube is

a√3 = √192

Or, a = √192/√3

Or, a = √64 = 8 cm

So, volume = a^{3} = 8^{3} = 512 cm^{3}

Workspace

The area of a parallelogram is 72 cm^{2} and its altitude is twice the corresponding base. What is the length of the base?

A.

10 cm

B.

8 cm

C.

6 cm

D.

5 cm

Answer with explanation

Answer: Option CExplanation

Area of a parallelogram, A =bh

where b is the base and h is the height of the parallelogram.

Let base =x cm.

Then, height =2x cm (∵ altitude is twice the base)

Workspace

A plot of land in the form of a rectangle has dimensions 240m x 180m. A drain 10m wide is dug all around it on the outside and the earth dug out is evenly spread over the plot increasing its surface level by 25cm. The depth of the derailment of ?

A.

1.225m

B.

1.229m

C.

1.233m

D.

1.227m

Answer with explanation

Answer: Option DExplanation

Outer length =(240 +20)m = 260m

Outer breadth =(180+20)m = 200m

Area of drailent =[(260 x 200) – (240 x 180)]m^{2}

= (52000 – 43200)m^{2} = 8800m^{2}

Let the depth of the derailment be x meters, then

==>> 8800 × x = 240 x 180 x 25/100

=> x = [60 * 180]/8800 m = 27/22 cm = 1.227m

Workspace

A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per sq.m is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.

A.

l=5; b=18; H=18

B.

l=6; b=18; H=15

C.

b=5; l=6; H=18

D.

b=6; l=18; H=6

Answer with explanation

Answer: Option DExplanation

Let breadth = x metres, length = 3x metres, height = H metres.

Area of the floor=(Total cost of carpeting)/(Rate) = (270/5) sq.m = 54 sq.m

So, breadth = 6 m and length =3(6)/2= 9 m.

Now, papered area = (1720/10) = 172 sq.m

Area of 1 door and 2 windows = 8 sq.m

Total area of 4 walls = (172 + 8) sq.m = 180 sq.m

==>> 2 * (9 + 6)H = 180

==>> H = 6

Therefore, b=6; l=18; H=6

Workspace

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A.

436

B.

336

C.

236

D.

338

Answer with explanation

Answer: Option BExplanation

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

s=1/2 x (30+14+40) = 42

==>> Area of parallelogram ABCD = 2 x 168 = 336 sq m

Workspace

A man riding a bicycle completes one lap of a circular field along its circumference at the speed of 14.4 km/h in 1 minute 28 seconds. What is the area of the field?

A.

6985 sq m

B.

7958 sq m

C.

9856 sq m

D.

8842 sq m

Answer with explanation

Answer: Option CExplanation

Workspace

When folded into two equal halves a rectangular sheet had a perimeter of 48cm for each part folded along one set of sides and the same is 66cm when folded along the other set of sides. Find the area of the sheet.

A.

1325

B.

750

C.

1584

D.

1120

Answer with explanation

Answer: Option DExplanation

Let the sheet be folded along its breadth and its perimeter = 48cm

Therefore, (l/2 + b) = 48 …… (i)

Now, let the sheet be folded along its length, and the perimeter = 66cm

(l + b/2)= 66 …… (ii)

Solving (i) and (ii), we get,

l = 56cm, b = 20cm

Area = l*b

Area = 1120 cm^{2}

Workspace

A Rectangular mat has an area of 150 sq.meters and perimeter of 46 m. Find the Length of its diagonal?

A.

17 cm

B.

17 m

C.

16 m

D.

17 m^{2}

Answer with explanation

Answer: Option BExplanation

rectangular area = l × b = 120 and perimeter = 2(l+b) = 46

l+b = 23

(l-b)^{2} – 4lb = (23)^{2} – 4 × 120 = (529-480) = 49 = l-b = 7

l+b = 23, l-b = 7, we get l = 15, b = 8

Diagonal = √15^{2}+8^{2}

√225+64 => √289 = 17 m

Workspace

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