The first pattern of triangles it uses 4 matches ( 3 matches for build a triangle and 1 matches for connected to other triangles).
a)Find the number of triangles if
there are 100 matches?
b) write the formulas
To find the number of triangles with a given number of matches, we can use the following formula:
n = (m - 1) / 4
where:
n is the number of triangles
m is the total number of matches
Let's apply this formula to the given scenario:
a) If there are 100 matches, we can substitute m = 100 into the formula:
n = (100 - 1) / 4
n = 99 / 4
n ≈ 24.75
Since we can't have a fraction of a triangle, we need to round down the result. Therefore, there would be 24 triangles if there are 100 matches.
b) The formula to find the number of triangles given the number of matches is:
n = (m - 1) / 4
where n is the number of triangles and m is the total number of matches.
a) To find the number of triangles that can be formed with 100 matches, we need to determine how many triangles can be formed with 4 matches and then multiply that by the number of sets of 4 matches that can be made with 100 matches.
Since each triangle requires 3 matches, the number of triangles that can be formed with 4 matches is 4 / 3 = 1 (ignoring any remaining matches).
To find the number of sets of 4 matches that can be made with 100 matches, we divide 100 by 4: 100 / 4 = 25.
So, the total number of triangles that can be formed with 100 matches is 1 * 25 = 25.
b) The formula for calculating the number of triangles that can be formed given the number of matches is:
Number of Triangles = (Number of Matches / 4) * (3 / 2)
Here, (Number of Matches / 4) represents the number of sets of 4 matches that can be made, and (3 / 2) represents the number of triangles that can be formed with a set of 4 matches.