A rectangle has an area of 72 square feet and a lengh 8 times greater than its width. what is the perimeter of the rectangle

Step-by-step explanation:

width = x  ft

Length = 8x

Area of rectangle = 72 sq.feet

length * width = 72

8x * x = 72

8x² = 72

x² = 72/8

x² = 9 = 3²

x = 3

Width = x = 3 feet

Length = 8x = 8*3 = 24 feet

Perimeter = 2*(length + width)

               = 2*(24 + 3) = 2*27 = 54 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.