- 1. The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.

A.) 120 m

B.) 121 cm

C.) 121 m

D.) None of these

Answer: Option 'C'

Let 6x and 5x be sides of the rectangle

6x × 5x = 1331

11x^{2} = 1331

x^{2} = 1331/11 = 121 => x = 11

Length = 6x = 6 × 11 = 66

Breadth = 5x => 5 × 11 = 55

Perimeter = 2 (l+b) => 2 (66+55) = 121 m

- 2. A rectangle measures 8 Cm on length and its diagonal measures 17 Cm. What is the perimeter of the rectangle?

A.) 46 cm

B.) 48 cm

C.) 46 m

D.) None of these

Answer: Option 'C'

Second side = √17^{2}-8^{2}

= √289-64

= 15 cm

Perimeter = 2 (l+b) = 2(8+5) Cm = 2(23) = 46 Cm

- 3. A rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is:

A.) 350

B.) 450

C.) 460

D.) 470

Answer: Option 'B'

l = 378 Cm and b = 525 Cm

Maximum length of a square tile

= HCF of (378,525) = 21 Cm

Number of tiles = (378×525)/(21×21) = (18×25) = 450

- 4. The ratio of the areas of two squares, one having double its diagonal then the other is:

A.) 1 : 3

B.) 3 : 1

C.) 1 : 4

D.) 4 : 1

Answer: Option 'D'

Lenth of the diagonals be 2x and x units.

areas are 1/2 × (2x)^{2} and (1/2 × x^{2})

Required ratio = 1/2 × 4 x^{2} : 1/2 x^{2} = 4 : 1

- 5. A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is:

A.) 17 cm

B.) 17 m

C.) 17 m^{2}

D.) 16 m

Answer: Option 'B'

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

- 6. The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.

A.) Rs. 25660

B.) Rs. 25560

C.) Rs. 25650

D.) Rs. 26550

Answer: Option 'C'

Area = 6 × 4.75 sq. metre.

Cost for 1 sq. metre. = Rs. 900

Hence total cost = 6 × 4.75 × 900 = 6 × 4275 = Rs. 25650

- 7. The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?

A.) 20 metres

B.) 25 metres

C.) 27 metres

D.) 18 metres

Answer: Option 'A'

Answer: Option 'A'

lb = 460 m^{2}...(Equation 1)

Let the breadth = b

Then length, l = b × (100+15)/100 = 115b/100 ...(Equation 2)

From Equation 1 and Equation 2,

115b/100 × b = 460

b2 = 46000/115 = 400

⇒ b = √400 = 20 m

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