Martina is making a small sign in the shape of a triangle for her store. She wants the height of the triangle to be 12 inches. The area of the sign must be less than 30 square inches. (Martina doesn't want to buy more material.) Write an inequality that describes the possible base lengths (in inches) of the triangle. Use b for the base length of the triangular sign.

To determine the possible base lengths \( b \) for Martina's triangular sign, we'll use the formula for the area of a triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Given: - Height (\( h \)) = 12 inches - Area must be less than 30 square inches Plugging the known values into the area formula: \[ \frac{1}{2} \times b \times 12 < 30 \] Simplify the inequality: \[ 6b < 30 \] Now, solve for \( b \): \[ b < \frac{30}{6} \] \[ b < 5 \] **Inequality:** \[ b < 5 \] This means the base length \( b \) must be **less than 5 inches** to ensure the area of the triangular sign stays under 30 square inches.