Question

the tile along the edge of a triangular community pool needs to be replaced. which expression represents the total perimeter of the pool edge? image of a right triangle labeled: one leg is $4x^2 + 15$, another leg is $8x + 10$, hypotenuse is $8x^2$ options: $12x^2 + 15$, $20x^2 + 25$, $12x^2 + 8x + 25$, $24x^2 + 16x + 50$

Explanation:

Step1: Recall Perimeter of Triangle

The perimeter \( P \) of a triangle is the sum of its three sides. For this right - triangle, the three sides are \( 4x^{2}+15 \), \( 8x + 10 \), and \( 8x^{2} \). So, \( P=(4x^{2}+15)+(8x + 10)+(8x^{2}) \).

Step2: Combine Like Terms

First, combine the \( x^{2} \) terms: \( 4x^{2}+8x^{2}=12x^{2} \).
Then, the \( x \) term: there is only one \( x \) term, which is \( 8x \).
Next, combine the constant terms: \( 15 + 10=25 \).
Putting it all together, we get \( P = 12x^{2}+8x + 25 \).

Answer:

\( 12x^{2}+8x + 25 \) (corresponding to the option "12\(x^{2}\) + 8x + 25")