shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. she decides to…

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 2l + 2w = 62 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
Answer:
- C. The value of (w) cannot be a negative number.
- D. Substitution is used to replace the variable (l) with a value of 20.
- E. The subtraction property of equality is used to isolate the term with the variable (w).
Explanation:
Step1: Analyze perimeter formula
The perimeter of a rectangle is (P = 2l+2w). Given (P = 62) and (l = 20), we have (62=2\times20 + 2w).
Step2: Analyze non - negativity of width
Width (w) represents a physical dimension, so (w\geq0), it can't be negative.
Step3: Analyze substitution
We substitute (l = 20) into the perimeter formula (2l + 2w=62).
Step4: Analyze solving for (w)
Starting with (62=40 + 2w), we use the subtraction property of equality. Subtract 40 from both sides: (62-40=40 + 2w-40), which simplifies to (22 = 2w).