Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from **Mensuration** that are important for all the competitive exams. We have included some questions that are repeatedly asked in exams !!

**In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 4m their ratio becomes 10:7. The area of the original rectangle in m² is?**

A. 846

B. 864

C. 840

D. 876

E. None of the Above

###### Answer & Explanation

Answer –**B. 864m²**

**Explanation :**

[3x + 4 / 2x + 4] = 10/7

x = 12

Area of the original rectangle = 3x * 2x = 6x²

Area of the original rectangle = 6 * 144 = 864m²**The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 500 cm. If the area of the rectangle is less than that of a Square then find the area of the rectangle?**

A. 1800 cm²

B. 1500 cm²

C. 1100 cm²

D. 1600 cm²

5. None of these

###### Answer & Explanation

Answer –**C.1100 cm²**

**Explanation :**

Perimeter of rectangle = Perimeter of Square = 160

4a = 160 => a = 40

Area of square = 1600

1600 – lb = 500

lb = 1100 cm²**Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 441 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?**

A. 354.5

B. 346.5

C. 316.5

D. 312.5

E. None of the Above

###### Answer & Explanation

Answer –**B. 346.5**

**Explanation :**

Area = 441 cm²

a = 21 cm

Perimeter of Square = 4 * 21

Circumference of a Circle = 4 * 21 * 22/7

2πr = 4 * 3 * 22

r = 12 * 22 * 7 / 2 * 22 = 42 cm

Radius of Circle B = 42/4 = 10.5 cm

Area of Circle = πr² = 22/7 * 10.5 * 10.5 = 346.5 cm²**The area of a rectangle is equal to the area of a square whose diagonal is 12√2 metre. The difference between the length and the breadth of the rectangle is 7 metre. What is the perimeter of rectangle ? (in metre).**

A. 68 metre

B. 50 metre

C. 62 metre

D. 64 metre

E. None of the Above

###### Answer & Explanation

Answer –**B. 50 metre**

**Explanation :**

d = a√2

12√2 = a√2

a = 12

l * b = a² = (12²) = 144

l – b = 7 ; l = b + 7

(b + 7)*(b) = 144

b² + 7b – 144 = 0

b = 9; l = 16

2(l + b) = 2(16 + 9) = 50m**The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the area of the rectangle?**

A. 159 m

B. 179 m

C. 147 m

D. 153 m

E. None of the Above

###### Answer & Explanation

Answer –**D. 153 m**

**Explanation :**

Length = x; Breadth =y

xy – (x-5)(y+3) = 9

3x – 5y – 6 = 0 —(i)

(x+3)(y+2) – xy = 67

2x + 3y -61 = 0 —(ii)

solving (i) and (ii)

x = 17m ; y = 9m

Area of the Rectangle = 153 m**The length of a plot is four times its breath. A playground measuring 900 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?**

A. 150

B. 130

C. 160

D. 140

E. 120

###### Answer & Explanation

Answer –**E. 120**

**Explanation :**

Area of the plot = (4 x 900) m²

= 3600 m²

Breadth = y meter

Length = 4y meter

Now area = 4y x y = 3600 m²

⇒ y² = 900 m²

⇒ y = 30 m

∴ Length of plot = 4y =120 m**The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the radius and height of the cylinder?(in m)**

A. 12, 7

B. 11, 8

C. 13, 6

D. 14, 5

E. 10, 9

###### Answer & Explanation

Answer –**D. 14, 5**

**Explanation :**

r + h = 19 m

2πr(r + h) = 1672

r = 1672 * 7/ 2 * 22 * 19 = 14

r = 14 ; h = 5**If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?**

A. 990m²

B. 900m²

C. 930m²

D. 945m²

E. None of the Above

###### Answer & Explanation

Answer –**B. 900m²**

**Explanation :**

(x+20) / x = 5 / 3

3x + 60 = 5x

x = 30m; Area = 900m²**The length of a park is four times of its breadth. A playground whose area is 1024 m² covers 1/4th part of the park. The length of the park is?**

A. 118 m

B. 142 m

C. 124 m

D. 126 m

E. 128 m

###### Answer & Explanation

Answer –**E. 128 m**

**Explanation :**

l = 4b

Area of the park = 4 * 1024 m²

l * b = 4 * 1024

l * l/4 = 4 * 4 * 1024

l² = 1024 * 16; l = 32 * 4 = 128 m**The width of a rectangular piece of land is 1/4 th of its length. If the perimeter of the piece of land is 320m its length is?**

A. 140 m

B. 128 m

C. 120 m

D. 156 m

E. 124 m

###### Answer & Explanation

Answer –**B. 128 m**

**Explanation :**

length = l ; breadth = l/4

2(l + b) = 320

2(l + l/4) = 320

l = 320 * 4/10 = 128m

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