Aptitude Questions – Mensuration Set 17

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1. The length of a rectangle wall is 3/2 times of its height. If the area of the wall is 600m². What is the sum of the length and height of the wall?
   A. 40
   B. 60
   C. 50
   D. 70
   E. None of the Above
   
   Answer & Explanation

   Answer – C. 50
   Explanation :
   length = 2x
   height = 3x
   Area of the wall = 3x * 2x = 6x² = 600
   x = 10; Sum of the length and height of the wall = 50
   
   
2. If the area of a circle is 616cm² whose diameter is equal to radius of a semicircle. Find the perimeter of the semicircle?
   A. 184 cm
   B. 154 cm
   C. 144 cm
   D. 164 cm
   5. None of these
   
   Answer & Explanation

   Answer – C. 144 cm
   Explanation :
   Area of a circle = 616cm²
   πr² = 616; r = 14
   D = Radius of Semi Circle = 28
   Perimeter of the semicircle = πr + 2r = 144cm
   
   
3. One side of rectangular ground is 8m and its diagonal is 17m. Find the area of ground?
   A. 150
   B. 140
   C. 130
   D. 120
   E. None of the Above
   
   Answer & Explanation

   Answer – D. 120
   Explanation :
   d = √(l² + b²)
   17 = √(l² + 8²)
   l² = 17² – 8² => l = 289  – 64 = 225
   l = 15
   Area = 15 * 8 = 120m²
   
   
4. The side of a square shaped garden is 8√2 . Find the maximum possible distancce between any two corners
   A. 18 metre
   B. 15 metre
   C. 16 metre
   D. 14 metre
   E. None of the Above
   
   Answer & Explanation

   Answer – C. 16 metre
   Explanation :
   d = a√2
   a = 8√2
   d = 16m
   
   
5. A rectangular ground 16m long and 10m breadth. It has a gravel path 2.5m wide all around it on the outside. What is the area of the path?
   A. 159 m²
   B. 155 m²
   C. 187 m²
   D. 183 m²
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 155 m²
   Explanation :
   Area of ground = 16 * 10 = 160
   Total area (ground + path) = (16 + 5)*(10 + 5) = 315
   Area of path = 315 – 160 = 155 m²
   
   
6. If the side of the square is increased by 30%, then how much % does its area get increased?
   A. 59%
   B. 69%
   C. 79%
   D. 49%
   E. None of these
   
   Answer & Explanation

   Answer – B. 69%
   Explanation :
   Area of the plot = 1.3 * 1.3 = 1.69 = 69%
   
   
7. A ladder is resting with one end in contact with the top of the wall of height 15m and the other end of the ground is at a distance 8m from the wall. The length of the ladder is?
   A. 17m
   B. 18m
   C. 16m
   D. 15m
   E. 10m
   
   Answer & Explanation

   Answer – A. 17m
   Explanation :
   Hypotenuse = √(base)² + (altitude)²
   √(8)² + (15)² = √289 = 17m
   
   
8. The perimeter of a square is equal to twice the perimeter of a rectangle of length 10 cm and breadth 4 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square?
   A. 38 cm
   B. 23 cm
   C. 46 cm
   D. 36 cm
   E. None of these
   
   Answer & Explanation

   Answer – D. 36 cm
   Explanation :
   Perimeter of square = 2(l + b)
   = 2 * 2(10 + 4) = 2 * 28 = 56 cm
   Side of square = 56/4 = 14 cm
   Radius of semi circle = 14/2 = 7cm
   Circumference of the semi-circle = 22/7 * 7 + 14 = 36 cm
   
   
9. The length of a rectangle is 3/5th of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?
   A. 112 cm²
   B. 149 cm²
   C. 189 cm²
   D. Cannot be determined
   E. None of these
   
   Answer & Explanation

   Answer – C. 189 cm²
   Explanation :
   Explanation :
   Circumference of the circle = 132
   2πR = 132; R = 21 cm
   Side of square = 21 cm
   Length of the rectangle = 3/5 * 21 = 63/5
   Area of the rectangle = 63/5 * 15 = 189 cm²
   
   
10. Smallest side of a right angled triangle is 13 cm less than the side of a square of perimeter 72 cm. Second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm. What is the largest side of the right angled triangle?
    A. 20 cm
    B. 12 cm
    C. 10 cm
    D. 13 cm
    E. None of these
    
    Answer & Explanation

    Answer – D. 13 cm
    Explanation :
    Explanation :
    Side of square = 72/4 = 18 cm
    Smallest side of the right angled triangle = 18 – 13 = 5 cm
    Length of rectangle = 112/8 = 14 cm
    Second side of the right angled triangle = 14 – 2 = 12 cm
    Hypotenuse of the right angled triangle = √(25 + 144) = 13cm