Question

select the correct answer.

the length, \\(l\\), of the shadow cast by an object varies directly as the height, \\(h\\), of the object. if \\(k\\) is the constant of variation, which equation represents this situation?

\\(l + h = k\\)
\\(lh = k\\)
\\(l = hk\\)
\\(l = h + k\\)

Explanation:

Identify the relationship between variables

The problem states that the length \(l\) varies directly as the height \(h\).

Formulate the direct variation equation

Using the constant of variation \(k\), a direct variation relationship between \(l\) and \(h\) is written as:

$$l = kh$$

Match with the given options

The equation \(l = kh\) is equivalent to \(l = hk\), which matches the third option.

Answer:

• (A) \(l + h = k\)
• (B) \(lh = k\)
• (C) \(l = hk\) (Correct answer)
• (D) \(l = h + k\)