Question

The height of a triangle is 2 less than 5 times its base. If the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?

Answer 1

To model the situation, we need to use the formula for the area of a triangle, which is given by:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case, we are given the following:

- The base of the triangle is \( x \) feet.
- The height of the triangle is \( 5x - 2 \) feet (since it is 2 less than 5 times the base).
- The area of the triangle is 12 square feet.

Now, we can substitute the values into the area formula:

\[
12 = \frac{1}{2} \times x \times (5x - 2)
\]

To eliminate the fraction, we can multiply both sides by 2:

\[
24 = x \times (5x - 2)
\]

Now, distribute \( x \):

\[
24 = 5x^2 - 2x
\]

Rearranging this equation gives us:

\[
5x^2 - 2x - 24 = 0
\]

Thus, the equation that models the situation is:

\[
5x^2 - 2x - 24 = 0
\]