Question

find the area of the triangle.
(triangle area $=\frac{1}{2}\cdot$ base $\cdot$ height)
the area of the triangle is (simplify your answer.)

Explanation:

Step1: Substitute the base and height into the formula

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = 4x - 3\) and the height \(h=10x\). So, \(A=\frac{1}{2}(4x - 3)\times10x\).

Step2: Simplify the expression

First, simplify \(\frac{1}{2}\times10x\). \(\frac{1}{2}\times10x = 5x\). Then, use the distributive property \(a(b - c)=ab-ac\), where \(a = 5x\), \(b = 4x\), and \(c = 3\). So, \(A=5x\times4x-5x\times3\).

Step3: Calculate each term

For \(5x\times4x\), using the rule \(a^m\times a^n=a^{m + n}\) (when \(a=x\), \(m = 1\), \(n = 1\)), we get \(5\times4\times x^{1+1}=20x^{2}\). For \(5x\times3 = 15x\).

Answer:

\(20x^{2}-15x\) square inches