Question

leila is making a pennant in the shape of a triangle for her senior class photo. she wants the base length of this triangle to be 6 inches. the area of the pennant must be at least 33 square inches. (the pennant has to be seen in the photo.) write an inequality that describes the possible heights (in inches) of the triangle. use h for the height of the triangular pennant.

Explanation:

Step1: Recall the area formula for a triangle

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

Step2: Substitute the given values into the formula

We know that $A\geq33$ (since the area must be at least 33 square - inches) and $b = 6$. Substituting these values into the formula, we get $\frac{1}{2}(6)h\geq33$.

Step3: Simplify the left - hand side of the inequality

$\frac{1}{2}(6)h=3h$. So the inequality becomes $3h\geq33$.

Step4: Solve for $h$

Divide both sides of the inequality $3h\geq33$ by 3. We get $h\geq11$.

Answer:

$h\geq11$