Question

question 4 (2 points)
which expression represents the area of the following triangle?
recall that the area of a triangle is \\(a = 1/2 bh\\)

image of a right-angled triangle with height \\(2x - 1\\) and base \\(x + 3\\)

\\(\bigcirc\\) \\(\frac{x^2 + 5x + 3}{2}\\)
\\(\bigcirc\\) \\(\frac{2x^2 + 6x - 3}{2}\\)
\\(\bigcirc\\) \\(\frac{2x^2 + 7x - 3}{2}\\)
\\(\bigcirc\\) \\(\frac{2x^2 + 5x - 3}{2}\\)

Explanation:

Identify base and height

Using the Quadratic Relations knowledge point

$$
LATEXBLOCK0
$$

Apply area formula

Using the Quadratic Relations knowledge point

$$ A = \frac{1}{2} \cdot b \cdot h = \frac{(x + 3)(2x - 1)}{2} $$

Expand the numerator

Using the Quadratic Relations knowledge point

$$
LATEXBLOCK1
$$

Write final expression

Using the Quadratic Relations knowledge point

$$ A = \frac{2x^2 + 5x - 3}{2} $$

Answer:

• (A) \(\frac{x^2 + 5x + 3}{2}\)
• (B) \(\frac{2x^2 + 6x - 3}{2}\)
• (C) \(\frac{2x^2 + 7x - 3}{2}\)
• (D) \(\frac{2x^2 + 5x - 3}{2}\) (Correct answer)