Question

Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation to find the width of the run. Which statements are true of the solution? Check all that apply. The value of w is 10 feet. The value of w can be zero. The value of w cannot be a negative number. Substitution is used to replace the variable l with a value of 20. The subtraction property of equality is used to isolate the term with the variable w.

Answer 1

Width of the rectangular Park = 11 feet

Explanation:

Given that the total length of the fencing is 62 feet. As has to be fenced around a rectangular park , it would be the perimeter of the rectangular park.

Also Shana wants the length of the run to be 20 feet. Hence the length of the park is 20 feet.

Here we will use the formula for perimeter to find the width of the run

Perimeter = 2(l+w)

62=2(l+w)

l+w =
`(62)/(2)`

l+w=31

20+w=31

w=31-20

w=11

Hence the width of the run for her dog in park would be 11 feet.

Answer 2

The correct options are C, D and E.

Explanation:

Consider the provided information.

Perimeter of a rectangular field is:

`P= 2 (length) + 2( width)\\P= 2 l + 2w`

Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet.

Substitute the L=20 and P=62 in above formula.

`P= 2 l + 2w`

`62= 2 (20) + 2w`

`62= 40 + 2w`

Isolate the variable w by subtraction property of equality.

`62-40= 40-40 + 2w`

`22=2w`

`w=11`

Hence, the length of width is 11.

Now consider the provided options.

Option A) The value of w is 10 feet.

This option is incorrect as the value of w is 11.

Option B) The value of w can be zero.

This option is incorrect as the value of w is 11.

Option C) The value of w cannot be a negative number.

This option is correct as the value of w is a positive number and length cannot be a negative number.

Option D) Substitution is used to replace the variable l with a value of 20.

This option is correct as we substitute L=20 in above calculation.

Option E) The subtraction property of equality is used to isolate the term with the variable w.

This option is correct as we use the subtraction property of equality in above calculation.

Hence, the correct options are C, D and E.