the tile along the edge of a triangular community pool needs to be replaced. which expression represents the…

the tile along the edge of a triangular community pool needs to be replaced. which expression represents the total perimeter of the pool edge? 12x² + 15 20x² + 25 12x² + 8x + 25 24x² + 16x + 50

the tile along the edge of a triangular community pool needs to be replaced. which expression represents the total perimeter of the pool edge? 12x² + 15 20x² + 25 12x² + 8x + 25 24x² + 16x + 50

Answer

Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter (P) of a triangle is (P=a + b+ c), where (a), (b), and (c) are the side - lengths of the triangle. Here, (a = 4x^{2}+15), (b=8x + 10), and (c = 8x^{2}).

Step2: Substitute the side - lengths into the perimeter formula

[ \begin{align*} P&=(4x^{2}+15)+(8x + 10)+8x^{2}\ \end{align*} ]

Step3: Combine like terms

Group the (x^{2}) terms, the (x) terms, and the constant terms:

  • For the (x^{2}) terms: (4x^{2}+8x^{2}=(4 + 8)x^{2}=12x^{2})
  • For the (x) terms: There is only one (x) term, which is (8x)
  • For the constant terms: (15 + 10=(15+10)=25)

So, (P=12x^{2}+8x + 25)

Answer:

(12x^{2}+8x + 25) (the third option)