Answer:
The number of posts required to fence the field are;
136 posts
Step-by-step explanation:
The measure of the rectangular field is given as follows;
The length of the rectangular field = 616 m
The width of the rectangular field = 456 m
Let 'x' represent the 'furthest distance possible between the posts
There will be one post at each of the four corners of the field
Let 'c' represent the number of posts at the four corners of the field
Therefore, the number of posts at the corner of the field, c = 4
Therefore, 'x' is highest common factor of 616 and 456
The prime factorization of 616 = 2³ × 7¹ × 11¹
The prime factorization of 456 = 2³ × 9 × 19
Therefore, the highest common factor of 616 and 456 = 2³ = 8
The distance between posts = 8 m
Let 'w' represent the number of posts on the 456 m side of the field less the posts at the corner corner of the field and let 'l' represent the number of posts on the 616 m side of the field less the posts at the corner corner of the field, we have;
The number of posts on the 456 m side less the corner post, w = 456/8 - 1 = 57 - 1 = 56
The number of posts on the 616 m side less the corner post, l = 616/8 - 1 = 77 - 1 = 76
The total number of posts required to fence the field, T = w + l + c
∴ T = 56 + 76 + 4 = 136
The total number of posts required to fence the field, T = 136 posts
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