Area Questions Answers

• 8. A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

  1. 10 m * 5 m
  2. 15 m * 5 m
  3. 20 m * 5 m
  4. 25 m * 5 m

  Answer And Explanation

  Answer: Option C

  Explanation:

  From the question, 2b+l = 30
  => l = 30-2b
  $$\begin{aligned} Area = 100m^2 \\ => l \times b = 100 \\ => b(30-2b) = 100 \\ b^2 - 15b + 50 = 0 \\ =>(b-10)(b-5)=0 \\ \end{aligned}$$
  b = 10 or b = 5
  when b = 10 then l = 10
  when b = 5 then l = 20
  Since the garden is rectangular so we will take value of breadth 5.
  So its dimensions are 20 m * 5 m

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• 9. A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is :

  1. 16000
  2. 18000
  3. 20000
  4. 22000

  Answer And Explanation

  Answer: Option C

  Explanation:

  $$\begin{aligned} \text{Number of bricks =}\frac{\text{Courtyard area}}{\text{1 brick area}} \\ = \left( \frac{2500 \times 1600}{20 \times 10} \right) \\ = 20000 \end{aligned}$$

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• 10. The length of a rectangle is three times of its width. If the length of the diagonal is $$\begin{aligned}8\sqrt{10}\end{aligned}$$ , then find the perimeter of the rectangle.

  1. 60 cm
  2. 62 cm
  3. 64 cm
  4. 66 cm

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let Breadth = x cm,
  then, Length = 3x cm
  $$\begin{aligned} x^2+{(3x)}^2 = {(8\sqrt{10})}^2 \\ => 10x^2 = 640 \\ => x = 8 \\ \end{aligned}$$
  So, length = 24 cm and breadth = 8 cm
  Perimeter = 2(l+b)
  = 2(24+8) = 64 cm

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• 11. A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is ?

  1. 25%
  2. 26%
  3. 27%
  4. 28%

  Answer And Explanation

  Answer: Option D

  Explanation:

  Let original length = x
  and original width = y
  Decrease in area will be
  $$\begin{aligned} = xy-\left( \frac{80x}{100}\times\frac{90y}{100}\right) \\ = \left(xy- \frac{18}{25}xy\right) \\ = \frac{7}{25}xy \\ \text{Decrease = }\left(\frac{7xy}{25xy} \times100\right) \% \\ = 28\% \end{aligned}$$

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• 12. What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Rs. 10 per square meter ?

  1. Rs. 3430
  2. Rs. 3440
  3. Rs. 3450
  4. Rs. 3460

  Answer And Explanation

  Answer: Option B

  Explanation:

  In this question, we are having perimeter.
  We know Perimeter = 2(l+b), right
  So,
  2(l+b) = 340
  As we have to make 1 meter boundary around this, so
  Area of boundary = ((l+2)+(b+2)-lb)
  = 2(l+b)+4 = 340+4 = 344
  
  So required cost will be = 344 * 10 = 3440

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• 13. The perimeters of 5 squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The perimeter of another square equal in area to the sum of the area of these square is:

  1. 124 cm
  2. 120 cm
  3. 64 cm
  4. 56 cm

  Answer And Explanation

  Answer: Option A

  Explanation:

  Clearly first we need to find the areas of the given squares, for that we need its side.
  
  Side of sqaure = Perimeter/4
  
  So sides are,
  
  $$\begin{aligned} \left(\frac{24}{4}\right),\left(\frac{32}{4}\right),\left(\frac{40}{4}\right),\left(\frac{76}{4}\right),\left(\frac{80}{4}\right) \\ = 6,8,10,19,20 \\ \text{Area of new square will be }\\ = [6^2+8^2+10^2+19^2+20^2] \\ = 36+64+100+361+400 \\ = 961 cm^2 \\ \text{Side of new Sqaure =}\sqrt{961} \\ = 31 cm \\ \text{Required perimeter =}(4\times31) \\ = 124 cm \end{aligned}$$

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• 14. 50 square stone slabs of equal size were needed to cover a floor area of 72 sq.m. Find the length of each stone slab.

  1. 110 cm
  2. 116 cm
  3. 118 cm
  4. 120 cm

  Answer And Explanation

  Answer: Option D

  Explanation:

  Area of each slab =
  $$\begin{aligned} \frac{72}{50}m^2 = 1.44 m^2\\ \text{Length of each slab =}\sqrt{1.44} \\ = 1.2m = 120 cm \end{aligned}$$

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