The perimeter of a rectangle is 18x – 24 and the width is
2x – 9. What is the length?
A: -7x + 3
B: 16x + 15
C: 7x - 3
D: 7x + 3

C

Step-by-step explanation:

18x - 24 = 2 [length + 2x - 9]

9x - 12 = length + 2x - 9

Length = 7x - 3

C: 7x - 3

Step-by-step explanation:

The perimeter of a rectangle is  given by

P = 2(l+w) where l is the length and w is the width

We know the perimeter is 18x -24 and the width is 2x-9.  Substituting these values into the equation

18x-24 = 2( l+2x-9)

Divide each side by 2

(18x-24)/2 = 2/2( l+2x-9)

9x-12 = l+2x-9

Add 9 to each side

9x-12 +9 = l+2x-9+9

9x -3 = l+2x

Subtract 2x from each side

9x-2x-3 = l+2x-2x

7x -3 = l

The length is 7x-3

∠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.