Question

the diagram shows the plans for the triangular park. what is the perimeter of the park? the perimeter is \boxed{} $x^2 + \boxed{} x - (\boxed{})$ feet. done \
(12x) ft \
(10x + 3x^2 - 8) ft \
(15x + 4) ft

Explanation:

Step1: Recall the perimeter formula for a triangle

The perimeter \( P \) of a triangle is the sum of the lengths of its three sides. So, we need to add the lengths of sides \( AB \), \( BC \), and \( AC \).
The lengths of the sides are: \( AB = 12x \) ft, \( BC=(10x + 3x^{2}-8)\) ft, and \( AC=(15x + 4)\) ft.
So, \( P=AB + BC+AC=12x+(10x + 3x^{2}-8)+(15x + 4) \).

Step2: Combine like terms

First, combine the \( x^{2} \) terms: There is only one \( x^{2} \) term, which is \( 3x^{2} \).
Next, combine the \( x \) terms: \( 12x+10x + 15x=(12 + 10+15)x = 37x \).
Then, combine the constant terms: \( - 8+4=-4 \).

Putting it all together, we get \( P = 3x^{2}+37x - 4 \).

Answer:

The perimeter is \( 3x^{2}+37x - 4 \) feet. So the boxes should be filled with 3, 37, and 4 respectively.