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Maths Case study (4 Marks)

Triangles · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 5 questions.

Questions

Case study (4 Marks)

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5 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below. To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12m, connecting C to point D at a distance of 40m from point C and the connecting D to the point A which is are a distance of 30m from D such the $\angle ADC=90^0.$
  1. Which property of geometry will be used to find the distance AC?
  2. Find the length AB?
  3. Which is the following does not form a Pythagoras triplet?
    Or
    Find the length of the rope used.
Answer
1. Pythagoras Theorem2. 38m
3. (21, 20, 28)
Or
82m
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Question 24 Marks

An aeroplane leaves an Airport and flies due north at 300km/ h. At the same time, another aeroplane leaves the same Airport and flies due west at 400km/ h.
  1. Which of the following line segment shows the distance between both the aeroplane?
  2. Distance travelled by the first aeroplane in 1.5 hours
  3. Which aeroplane travelled a long distance and by how many km?
    Or
    How far apart the two aeroplanes would be after 1.5 hours?
Answer
1. AB2. 450 Km
3. Second, 150km
Or
750 Km
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Question 34 Marks

Minister of a state went to city Q from city P. There is a route via city R such that $\text{PR}\perp\text{RQ}$ PR = 2xkm and RQ = 2(x + 7)km. He noticed that there is a proposal to construct a 26km highway which directly connects the two cities P and Q.

Based on the above information, answer the following questions.
  1. Which concept can be used to get the value of x is?
  2. The value of x is ?
  3. The value of PR is?
    Or
    How much distance will be saved in reaching city Q after the construction of highway?
Answer
1. Pythagoras theorem2. 5
3. 10 Km
Or
8 Km
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Question 44 Marks

Two hotels are at the ground level on either side of a mountain. On moving a certain distance towards the top of the mountain two huts are situated as shown in the figure. The ratio between the distance from hotel B to hut -2 and that of hut -2 to mountain top is 3 : 7.

Based on the above information, answer the following questions.
  1. What is the ratio of the perimeters of the triangle formed by both hotels and mountain top to the triangle formed by both huts and mountain top?
  2. What is the ratio of areas of two parts formed in the complete figure?
  3. The distance between the hotel A and hut -1 is ?
    Or
    lf the horizontal distance between the hut -1 and hut -2 is 8miles, then the distance between the two hotels is ?
Answer
1. 10 : 72. 49 : 51
3. 4.29 miles
Or
11.3 miles
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Question 54 Marks

Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure.
  1. In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called.
  2. Which is the correct similarity criteria applicable for smaller triangles at the upper part of this kite?
  3. Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles are in the ratio:
    OR
    What is the area of the kite, formed by two perpendicular sticks of length 6cm and 8cm?
Answer
1. The converse of Pythagoras theorem2. SAS
3. 4 : 9
Or
$48 cm^2$​​​​​​​
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