The length of rectangular sign is 12 less than twice the width. its perimeter is 114 ft. find the length and the width of the sign.

The sum of length and width of a rectangle is half the perimeter. Here the sum of length and width is 114/2 = 57 ft.

If we add 12 ft to this total, we have a value that is 3 times the width.

The width of the sign is 69 ft/3 = 23 ft.

The length of the sign is (2·23 -12) = 34 ft.

From the problem statement, using L and W for length and width:

... L = 2W -12

... P = 114 = 2(L +W)

Dividing the second equation by 2 and substituting for L, we have ...

... 57 = (2W -12) +W

... 69 = 3W . . . . . . . . add 12

... 23 = W . . . . . . . . . divide by 3

Width=23 Lengh=34

what does x eaqual

step-by-step explanation:

∠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.