Question

1. mathematical connections a triangle has a height of 2x + 6 and a base length of x + 4. what is the area of the triangle?

Explanation:

Step1: Recall area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Substitute values

Substitute $b = x + 4$ and $h=2x + 6$ into the formula: $A=\frac{1}{2}(x + 4)(2x + 6)$.

Step3: Expand the expression

First, expand $(x + 4)(2x + 6)$ using the FOIL method. $(x + 4)(2x+6)=x(2x)+x(6)+4(2x)+4(6)=2x^{2}+6x + 8x+24=2x^{2}+14x + 24$. Then, $A=\frac{1}{2}(2x^{2}+14x + 24)$.

Step4: Distribute the $\frac{1}{2}$

$A=\frac{1}{2}\times2x^{2}+\frac{1}{2}\times14x+\frac{1}{2}\times24=x^{2}+7x + 12$.

Answer:

$x^{2}+7x + 12$