Question

Susan is making a small sign in the shape of a triangle for her store. She wants the height of the triangle to be 8 inches. The area of the sign must be at most 36 square inches. Write an inequality that describes the possible base lengths (in inches) of the triangle. Use b for the base length of the triangular sign.

Answer 1

To find the possible base lengths of a triangular sign with a height of 8 inches and maximum area of 36 square inches, we write the inequality 36 ≥ 1/2 × b × 8, which simplifies to b ≤ 9. Thus, the base length must be 9 inches or less.

Step-by-step explanation:

Triangle Area and Inequality

The formula for the area of a triangle is Area = 1/2 × base × height. Susan wants the height of her triangular sign to be 8 inches and the area to be at most 36 square inches, we can set up an inequality to find the possible base lengths (b).

Area ≤ 1/2 × b × 8

Given the maximum area (A) to be 36 square inches:

36 ≥ 1/2 × b × 8

Multiplying each side of the inequality by 2 to remove the fraction, we get:

72 ≥ b × 8

Finally, divide each side of the inequality by 8 to solve for b:

b ≤ 9

So, the possible base lengths of Susan's sign must be 9 inches or less.