The problem states that the area of a triangular neon billboard is 76 square feet. The base of the triangle is 3 feet longer than twice the length of the altitude. Part (a) asks for the dimensions of the triangular billboard in feet. The altitude is given as 8 feet.

1. Problem Description

The problem states that the area of a triangular neon billboard is 76 square feet. The base of the triangle is 3 feet longer than twice the length of the altitude.

Part (a) asks for the dimensions of the triangular billboard in feet. The altitude is given as 8 feet.

2. Solution Steps

The altitude of the triangle is given as 8 feet. We are told the base is 3 feet longer than twice the length of the altitude. So, we can express the base, $b$, as

$b = 2 * altitude + 3 = 2 * 8 + 3 = 16 + 3 = 19$ feet.

We can check our answer using the area of a triangle formula:

$Area = \frac{1}{2} * base * altitude$

$Area = \frac{1}{2} * 19 * 8 = \frac{1}{2} * 152 = 76$ square feet. This matches the given area, so our base calculation is correct.

3. Final Answer

The length of the altitude of the triangular billboard is 8 feet.

The base of the triangular billboard is 19 feet.