Question

The altitude of a triangular banner is 4 feet longer than twice its base. Define the functions that describe the altitude and base of the triangle, and then use these functions to build an area function of the banner.

Answer 1

The functions that describe the altitude and base of the triangle are 'Altitude = 2b + 4' and 'Base = b'. The area function of the banner is 'Area = b^2 + 2b'.

Step-by-step explanation:

To define the functions that describe the altitude and base of the triangle, let's assume the base of the triangle is 'b' feet. According to the problem, the altitude is 4 feet longer than twice its base, so the altitude can be expressed as '2b + 4' feet. Therefore, the functions that describe the altitude and base of the triangle are:

Altitude = 2b + 4

Base = b

To build the area function of the banner, we can use the formula for the area of a triangle which is 1/2 × base × altitude. Substituting the functions for base and altitude into the area formula, we get:

Area = 1/2 × b × (2b + 4)

Expanding and simplifying the expression, we have:

Area = b^2 + 2b