Question

1. which of the following represents an expression for the area of the triangle shown below?

a. $3x - 1$
b. $2x^2 + 2x - 12$
c. $x^2 + 5x - 6$
d. $x^2 + x - 6$
(the triangle has a base of $2x - 4$ and a height of $x + 3$)

Explanation:

Step1: Recall the area formula for a triangle.

The area of a triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, the base is \( 2x - 4 \) and the height is \( x + 3 \).

Step2: Substitute the base and height into the formula.

\[

$$\begin{align*} A&=\frac{1}{2}\times(2x - 4)\times(x + 3)\\ &=\frac{1}{2}\times[2x(x + 3)-4(x + 3)]\\ &=\frac{1}{2}\times(2x^{2}+6x - 4x - 12)\\ &=\frac{1}{2}\times(2x^{2}+2x - 12)\\ &=x^{2}+x - 6 \end{align*}$$

\]

Answer:

d. \( x^{2}+x - 6 \)