The 3 by 3 grid below shows nine 1cm×1 cm squares and uses 24 cm of wire. What length of wire is required for a similar 20 by 20 grid?
Answers
Given:
24 cm of wire is used to make the grid of 3 by 3
To find:
The length of the wire used to make a grid of 20 by 20.
Solution:
1) To calculate the length of the wire we need to find the number of lines required to make the grid of 3 by 3.
2) From the given figure:
- Horizontal lines = 4
- Vertical lines = 4
- Total lines are 8
Means for the grid of n by n the number of lines used is 2(n+1).
So the length of a line will be 24/8 which is 3 cm
3) Now, we have to make the grid of 20 by 20 so the numbers of lines would be
- 2(20+1) = 42
So the total length of the wire would be 42×3 = 126cm.
The length of the wire used to make a grid of 20 by 20 is 126cm.
The length of the wire required for a similar 20 by 20 grid is 840 cm
Step-by-step explanation:
There are 9, 1 cm × 1 cm squares forming 3 × 3 grid
The length of wire required in 3 x 3 grid is
3(3+1) + 3(3+1)
= 3 × 4 + 3 × 4
= 24 cm
The length of the wire required in 20 by 20 grid
= 20(20+1) + 20(20+1)
= 20 × 21 + 20 × 21
= 420 + 420
= 840 cm
Hope this answer is helpful.
Know More:
Q: The wire is in shape of square of side 10 cm. If the wire is rebent into rectangle of length 12 cm find its breath which figure encloses more area and by how much?
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