Length of a rectangle is 5 cm longer than the width. four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. the total area of the constructed figure is 120 cm2. what is the perimeter of the rectangle?

The perimeter of rectangle is

Step-by-step explanation:

Let

x------> the length of rectangle

y----> the width of rectangle

we know that

The area of the constructed figure is equal to

so

-----> equation A

-----> equation B

substitute equation B in equation A

using a graphing calculator to resolve the quadratic equation

the solution is

Find the value of x

Find the perimeter of rectangle

The perimeter of rectangle is equal to

∠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.