Lenni has a rectangular garden with a length of 5x-7 and a width of x-2. Write an expression for the total perimeter in terms of x.


Lenni measured the perimeter to be 66 feet. What is the value of x? Enter a number only in the box below.

feet

P = 12x - 18, x = 7 feet

Step-by-step explanation:

We know that the formula for the perimeter of a rectangle is:

Where l is the length and w is the width. So we just substitute in for variables:

P = 2 (5x - 7) + 2 (x - 2)

We distribute by foiling:

P = 10x - 14 + 2x - 4

Then combine like terms:

P = 12x - 18

This can be further factored to 6(2x - 3) if needed.

Since we know the expression for perimeter, we can just set it equal to 66 feet, like this:

6(2x - 3) = 66

Divide both sides by 6:

2x - 3 = 11

Add 3 to both sides:

2x = 14

Divide both sides by 2:

x = 7 feet

∠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.