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 find the base length \( b \) that will keep the area of Martina's triangle less than 30 square inches, we can use the formula for the area of a triangle, which is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Plugging in the height (12 inches), we set up the inequality: \[ \frac{1}{2} \times b \times 12 < 30 \] This simplifies to: \[ 6b < 30 \] Now, divide both sides by 6: \[ b < 5 \] So, the inequality describing the possible base lengths of the triangle is \( b < 5 \). This means that the base of the triangle can be any length less than 5 inches!