Asked by Alto saxaphone
The area of a rectangular trampoline is 112 ft2
. The length of the trampoline is 6 ft greater than the width of the trampoline. This situation can be represented by the equation w2+6w−112=0
.
What is the width of the trampoline in feet?
(1 point)
8 ft
14 ft
16 ft
7 ft
For the incorrect answers, what mistake would you have to make to get that answers
All Answers 1
Answered by
GPT-5 mini
AI
Answer: 8 ft.
Work: w^2 + 6w − 112 = 0 factors as (w − 8)(w + 14) = 0, so w = 8 or w = −14. Width must be positive, so w = 8 ft.
Mistakes that would give the incorrect choices:
- 14 ft: Taking the negative root −14 and reporting its absolute value 14, or factoring with the wrong sign (e.g. (w + 8)(w − 14) ) and choosing 14.
- 16 ft: Using the quadratic formula but forgetting to divide by 2: (-6 + 22) = 16 instead of [(-6 + 22)/2] = 8.
- 7 ft: Picking the factor pair 7 and 16 because 7·16 = 112 and (incorrectly) assuming those differ by 6, then choosing the smaller factor 7.
Work: w^2 + 6w − 112 = 0 factors as (w − 8)(w + 14) = 0, so w = 8 or w = −14. Width must be positive, so w = 8 ft.
Mistakes that would give the incorrect choices:
- 14 ft: Taking the negative root −14 and reporting its absolute value 14, or factoring with the wrong sign (e.g. (w + 8)(w − 14) ) and choosing 14.
- 16 ft: Using the quadratic formula but forgetting to divide by 2: (-6 + 22) = 16 instead of [(-6 + 22)/2] = 8.
- 7 ft: Picking the factor pair 7 and 16 because 7·16 = 112 and (incorrectly) assuming those differ by 6, then choosing the smaller factor 7.
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