kyla makes a triangular school pennant. the area of the triangle is 180 square inches. the base of the…

Explanation:

Step1: Define base and height expressions

Let the base $b = z$. The height $h=2z + 6$. The area formula is $A=\frac{1}{2}bh$, and $A = 180$.

Step2: Substitute into area formula

Substitute $b = z$, $h=2z + 6$ and $A = 180$ into $A=\frac{1}{2}bh$. We get $180=\frac{1}{2}z(2z + 6)$.

Step3: Simplify the equation

First, multiply both sides by 2 to get rid of the $\frac{1}{2}$: $360=z(2z + 6)$. Expand the right - hand side: $360 = 2z^{2}+6z$. Rearrange to standard quadratic form: $2z^{2}+6z - 360=0$. Divide through by 2: $z^{2}+3z - 180=0$.

Step4: Solve the quadratic equation

Factor the quadratic equation: $(z + 15)(z - 12)=0$. So $z=-15$ or $z = 12$. Since length cannot be negative, $z = 12$.

Step5: Find the height

Since $h=2z + 6$ and $z = 12$, then $h=2\times12+6=24 + 6=30$.

Answer:

30 inches