Question

Math

Posted 6 months ago

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Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden.
The graph below represents the widths that correspond to possible lengths of Lea's garden.
As the possible width of Lea's garden increases, what does its possible length approach?
Choose 1 answer:
(A) $\infty$
(B) 0
(C) 10
(D) $\mathbf{1 2 0}$
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

The graph shows that as $w$ increases, the curve approaches a horizontal line near the y-axis value of 10

step 3

This suggests that the length $l$ approaches a value close to 10 as the width $w$ becomes larger

step 4

Since the area of the garden is 100 square meters, the relationship between the width $w$ and length $l$ must satisfy the equation $w \cdot l = 100$

step 5

As $w$ increases, $l$ must decrease to maintain the constant area of 100 square meters, but the graph indicates that $l$ does not decrease to 0

[question number] Answer

C

Key Concept

Asymptotic Behavior

Explanation

The length $l$ approaches a horizontal asymptote as the width $w$ increases, indicating that $l$ approaches a constant value.

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