Question

find the area of the triangle. simplify your answer.

Explanation:

Step1: Recall the formula for the area of a triangle

The area \( A \) of a triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, the base is \( 2x \) and the height is \( x - 7 \).

Step2: Substitute the base and height into the formula

Substitute base \( = 2x \) and height \( = x - 7 \) into the formula:
\( A=\frac{1}{2}\times(2x)\times(x - 7) \)

Step3: Simplify the expression

First, simplify \( \frac{1}{2}\times(2x) \), which is equal to \( x \). Then multiply by \( (x - 7) \):
\( A=x\times(x - 7)=x^{2}-7x \)

Answer:

\( x^{2}-7x \)