Final answer:
To find the perimeter of triangle HOP, we need to solve for x by simplifying and solving a quadratic equation. Then, substitute the value of x into the expression 3x+15 to find the length of one side. Finally, multiply the length of one side by 3 to get the perimeter of the triangle.
Step-by-step explanation:
To find the perimeter of triangle HOP, we first need to find the value of x. The given expression is (3x+15) (4x+12) (H p 18 in). It seems there might be a typo as 'H p 18 in' does not make sense. Assuming it's meant to be 'HP = 18 in', let's solve for x.
- Simplify the expression: (3x+15)(4x+12)=18.
- Expand and collect like terms: 12x²+76x+180=18.
- Subtract 18 from both sides of the equation: 12x²+76x+162=0.
- Factor the quadratic equation or use the quadratic formula to solve for x.
- Once you have the value of x, substitute it into the expression 3x+15 to find the length of one side of the triangle.
- Multiply the length of one side by 3 to get the perimeter of the triangle.