The area of a rectangle wall of a barn is 320 square feet. it's length is12 feet longer than twice it's width. find the length and width of the wall of the barn.

Length = 32 feet

Width = 10 feet

Step-by-step explanation:

The area of a rectangle = length (L) x width (W)

The relationship between the length and width is that

L = 12 + 2W (i)

therefore

Area = L x W can be rewritten as (12 + 2W) x W

320 =  (12 + 2W) x W

320 = 12W + 2W^2

this can then be turned into a quadratic equation:

2W^2 + 12W - 320 = 0

Divide through by 2

W^2 + 6W - 160 = 0

W^2 - 10W + 16W - 160 = 0

W(W- 10) + 16(W- 10) = 0

(W- 10)(W + 16) = 0

hence W = -16 and 10

since width cannot be a negative value,

Width = 10

hence substituting for width = 10 into equation (i)

L = 12 + 2(10)

L = 12 +20 = 32

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.