Question

4. A rectangular field measures, 616m by 456m. Fencing

Answer 1

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