Question

Rajeev and Sanjeev were feeling bored during the lockdown.They both created a number game. Sanjeev prepared nine equilateral triangles and numbered them 1 to 9 .The numbers written on the triangles also represented length of each side of the triangle (in cm) .Sanjeev arranged them in the form of a circle.He asked Rajeev to remove alternate triangle starting from number 1,going clockwise,until only one triangle remained
(1) The triangle which Rajeev removed in the first round are,in order,numbered 1,3,5,7,9...... If Rajeev continues in the same manner,which numbered triangle will be left in the last?
(a) 4 (b) 2 (c) 8 (d) 6

(2) In the second round,Sanjeev started counting with triangle numbered as 1and eliminated every third triangle,until only one triangle remained.Which of the following triangle will be left in the end?
Triangle no -
(a) 1 ( b) 3 (c) 7 (d) 6

(3) Rajeev added two more triangle in the circle and numbered these as triangle 10and triangle 11 .In this round, Rajeev started counting with triangle numbered as 1,but anti clockwise,and eliminated every fifth triangle,until only one triangle remained.Which triangle will be left in the end
(a) 4 (b) 2 (c) 8 (d) 5
(4) If there are 9 triangles,will the perimeters of the triangle follow any pattern? If so, write the pattern?


(5) The area of an equilateral triangle is found using under root 3 upon 4 (side)².Are the areas of the triangle numbered 3,4 and 6,8 in proportion? Justify your Answer


Give me Answer now ​

Answer 1

Given :  Sanjeev arranged 9 triangles in the form of a circle.

Rajeev  removed alternate triangles

The triangles which Rajeev removed in the first round are, in order, numbered 1, 3, 5, 7, 9,…

Rajeev continues in the same manner,

To Find : which numbered triangle will be left in the last?

a) 4

b) 2

c) 8

d) 6

Solution:

  1      2     3    4   5    6     7    8     9  

Removed         1, 3, 5, 7, 9,…  

then removed    4      8          

then removed    6  

2  numbered triangle will be left in the last

Learn More:

Rajeev continues in the same manner,

https://brainly.in/question/26113528

https://brainly.in/question/25501974

Answer 2

Answer:

Step-by-step explanation:

Question 1: b) 2

Question 2: a) 1

Question 3: d) 5

Question 4:

The perimeters will be 3cm, 6cm, 9cm, 12 cm….

They are multiples of 3 or increasing with a difference 3.

Question 5:

Area of these triangles are √3/4( 3)

2

, √3/4( 4)

2

, √3/4 (6)

2

, √3/4( 8)

2

,

Ratio of the areas of first two triangles is 9:16 and that of last two triangles is 36: 64 = 9: 16.

Hence, they are in proportion.