Question

the diagram shows the plans for the triangular park. how much longer is bc than ac? (3x² - 25x - 12) feet (3x² - 5x - 12) feet (3x² + 5x - 4) feet (3x² + 25x - 4) feet done the diagram has a right triangle abc with right angle at a. ab is (12x) ft, ac is (15x + 4) ft, and bc is (10x + 3x² - 8) ft. there is a circle inside the triangle.

Explanation:

Step1: Identify lengths of BC and AC

From the diagram, length of \( BC = (10x + 3x^2 - 8) \) ft and length of \( AC = (15x + 4) \) ft.

Step2: Subtract AC from BC

To find how much longer \( BC \) is than \( AC \), we calculate \( BC - AC \).
\[

$$\begin{align*} BC - AC&=(10x + 3x^2 - 8)-(15x + 4)\\ &=10x + 3x^2 - 8 - 15x - 4\\ &=3x^2+(10x - 15x)+(- 8 - 4)\\ &=3x^2 - 5x - 12 \end{align*}$$

\]

Answer:

\((3x^2 - 5x - 12)\) feet