Question

1. find an expression for the area of the triangle shown below. note that the height is x + 10 and the base is 5x - 4.

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Identify the base and height

Given that the base \(b = 5x - 4\) and the height \(h=x + 10\).

Step3: Substitute the values into the formula

Substitute \(b = 5x - 4\) and \(h=x + 10\) into \(A=\frac{1}{2}\times base\times height\).
We get \(A=\frac{1}{2}(5x - 4)(x + 10)\).

Step4: Expand the expression

Using the distributive property \((a - b)(c + d)=ac+ad - bc - bd\), where \(a = 5x\), \(b = 4\), \(c=x\), \(d = 10\).
\((5x-4)(x + 10)=5x\times x+5x\times10-4\times x - 4\times10=5x^{2}+50x-4x - 40=5x^{2}+46x - 40\).
Then \(A=\frac{1}{2}(5x^{2}+46x - 40)=\frac{5}{2}x^{2}+23x - 20\).

Answer:

\(\frac{5}{2}x^{2}+23x - 20\)