Jackson is building a small rectangular basketball section in his backyard. The length of the section will be 1.25 times the width of the section. Part A (2 POINTS) Create an equation to represent the area of the basketball section, A, in terms of the width, w. Part B (5 POINTS) Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?

Part A)

Part B) Length: 17.5 feet and Width: 14 feet

Step-by-step explanation:

Part A) Create an equation to represent the area of the basketball section A, in terms of the width W.

Let

L ----> the length of the  rectangular basketball section

W ---> the width of the  rectangular basketball section

we know that

The area of the rectangular basketball section is equal to

----> equation A

The length of the section will be 1.25 times the width of the section

so

----> equation B

substitute equation B in equation A

Part B) Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?

we have

so

solve for W

Find the value of L

substitute the value of W in the equation B

therefore

The dimensions are :

Length: 17.5 feet

Width: 14 feet

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.