Question

find the area. simplify your answer. x - 5 2x + 2

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is \( A=\frac{1}{2}\times base\times height \). Here, the base \( b = 2x + 2 \) and the height \( h=x - 5 \).

Step2: Substitute the values into the formula

Substitute \( b = 2x + 2 \) and \( h=x - 5 \) into \( A=\frac{1}{2}\times b\times h \), we get \( A=\frac{1}{2}(2x + 2)(x - 5) \).

Step3: Simplify the expression

First, factor out a 2 from \( 2x+2 \), so \( A=\frac{1}{2}\times2(x + 1)(x - 5) \). Then, the \( \frac{1}{2} \) and 2 cancel out, and we use the FOIL method \((a + b)(c + d)=ac+ad+bc+bd\) with \(a=x\), \(b = 1\), \(c=x\), \(d=-5\).
\(A=(x + 1)(x - 5)=x\times x+x\times(-5)+1\times x+1\times(-5)=x^{2}-5x+x - 5=x^{2}-4x - 5\)

Answer:

\(x^{2}-4x - 5\)