Question

Write a function rule for the area of a triangle with a base 3 cm greater than 5 time its height. What is the area of triangle when the height is 6 cm

Answer 1

f(h) = (5h² + 3h) / 2

f(6) = 99 cm²

Explanation:

Let's call this function f(h), as we are referring to the base of a triangle in terms of its height.

The equation for the area of a triangle is given by

A = (base * height) / 2

Let's denote height as h and base as b

base b = 5h + 3

Let's substitute base b in terms of h for our area equation

A = ((5h + 3) * h) /2

Expanding this

A = (5h² + 3h) / 2

Written as a function of height then we have

f(h) = (5h² + 3h) / 2

Let's solve for the area of a triangle then who's height is 6 cm

f(6) = (5(6)² + 3(6)) / 2

f(6) = (180 + 18) / 2

f(6) = 198 / 2

f(6) = 99 cm²