Geometry

Question Analysis  

The main focus is using Heron's formula to find the perimeter. Given the area and side - length ratio (5:5:6), we'll represent sides with a variable, calculate the semi-perimeter, apply Heron's formula to solve for the variable, and then determine the perimeter.

 

Key Concept Explanation  

Heron's Formula: For a triangle with side lengths , , , the area , where  (semi-perimeter). When side lengths are in a ratio, we can use a common variable  to represent them (, , ) and then apply the formula.

 

Step-by-Step Solution  

1. Represent the sides and find the semi-perimeter:  

Let the sides be , , .  

The perimeter , so the semi-perimeter .  

2. Apply Heron's formula:  

Substitute into Heron's formula:  

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