Question 11 - Figure it out - Page 102 to 105 - Chapter 4 Class 7 - Expressions using Letter-Numbers (Ganita Prakash)

Transcript

Question 11 Imagine a straight rope. If it is cut once as shown in the picture, we get 2 pieces. If the rope is folded once and then cut as shown, we get 3 pieces. Observe the pattern and find the number of pieces if the rope is folded 10 times and cut. What is the expression for the number of pieces when the rope is folded r times and cut?From images, we note that When a straight rope (0 folds) is cut once, you get 2 pieces When the rope is folded once (1) and then cut, you get 3 pieces When the rope is folded twice (2) and then cut, you get 4 pieces Observing this pattern, we notice that the number of pieces is always 2 more than the number of folds. The formula is: Number of pieces = r + 2, where 'r' is the number of folds. So, our expression is formed. Now, we need to find Number of pieces if folded 10 times: Number of pieces if folded 10 times: Since rope is folded 10 times, ∴ r = 10 Putting r = 10 in formula Number of pieces = 10 + r = 10 + 2 = 12 pieces