Mensuration Questions and Answers

Answer: A

Let the length and the breadth of the rectangle be 4x cm and 3x respectively.

(4x)(3x) = 6912

12x2 = 6912 

x2 = 576 = 4 * 144 = 22 * 122 (x > 0)

=> x = 2 * 12 = 24

Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.

Answer: D

Let the sides of the rectangle be l and b respectively.

From the given data, 

(√l² + b²) = (1 + 108 1/3 %)lb 

=> l² + b² = (1 + 325/3 * 1/100)lb

= (1 + 13/12)lb

= 25/12 lb

=> (l2 + b²)/lb = 25/12 

12(l2 + b²) = 25lb 

Adding 24lb on both sides 

12l2 + 12b² + 24lb = 49lb 

12(l2 + b² + 2lb) = 49lb 

but 2(l + b) = 28 => l + b = 14 

12(l + b)² = 49lb 

=> 12(14)² = 49lb 

=> lb = 48 

Since l + b = 14, l = 8 and b = 6 

l - b = 8 - 6 = 2m.

Answer: B

With \( l = 3b \):

\[ 3b \times b = 3b^{2} = 867 \quad\Longrightarrow\quad b^{2} = 289 \]

\[ b = 17 \text{ m} \]

The length is then 51 m, which is offered as a distractor for anyone who solves for the wrong side.

Answer: C

Let the length and the breadth of the floor be l m and b m respectively.

l = b + 200% of b = l + 2b = 3b

Area of the floor = 324/3 = 108 sq m

l b = 108 i.e., l * l/3 = 108

l2 = 324 => l = 18.

Answer: D

Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)

= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m

Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

Answer: A

Find the side, then the perimeter, then price it.

\[ \text{side} = \sqrt{289} = 17 \text{ ft} \]

\[ \text{perimeter} = 4 \times 17 = 68 \text{ ft} \]

\[ \text{cost} = 68 \times 58 = \text{Rs. } 3944 \]

The fence follows the boundary, so it is priced by perimeter, not area - the data are complete, so "cannot be determined" is a trap.

Answer: B

\[ \text{rectangle} = 125 \times 64 = 8000 \text{ cm}^{2} \]

\[ \text{square} = 5 \times 8000 = 40{,}000 \text{ cm}^{2} \]

\[ \text{side} = \sqrt{40000} = 200 \text{ cm} \]

\[ \text{perimeter} = 4 \times 200 = 800 \text{ cm} \]

The question asks for the perimeter, so the square root must be multiplied by four - stopping at the side gives 200.

Answer: B

The circumference of the circle is equal to the permeter of the rectangle. 

Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 

 =>  x = 1 

Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm²

Answer: D

\[ \text{side of square} = \sqrt{4096} = 64 \text{ cm} \]

\[ \text{length} = 2 \times 64 = 128 \text{ cm}, \qquad \text{breadth} = 64 - 24 = 40 \text{ cm} \]

\[ \text{breadth} : \text{length} = 40 : 128 = 5 : 16 \]

That ratio is not among the choices, so the answer is none of these. The 7 : 16 on offer is close enough to catch a careless division.

Answer: D

Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 

4a = 2(l + b) 

2a = l + b 

l . b = 480 

We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . 

Area of the square cannot be found.