A field in the shape of a quadrilateral has a perimeter of 166 m. A fence is being built along the field's perimeter. Determine the length of fencing needed for each side of the field.

3x - 4 =  32

2x =  24

5x + 10 = 70

4x - 8 = 40

Step-by-step explanation:

Please find the complete question in the attached image

Perimeter = sum of sides of the quadrilateral

166 = 4x - 8 + 5x + 10 + 2x + 3x - 4

166 = 14x - 2

combine like terms

166 + 2 = 14x

168 = 14x

x = 12

substitute for x in each of the sides

3x - 4 = 3(12) - 4 = 32

2x = 2 x 12 = 24

5x + 10 = 5(12) + 10 = 70

4x - 8 = 4(12) - 8 = 40

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6