Geometry

Question Analysis  

The problem gives the side lengths , ,  of triangle  and asks for the height  corresponding to side . The key is to first find the area of the triangle using Heron's formula and then use the area formula to determine .

 

Key Concept Explanation  

1. Heron's Formula: Used to find the area  of a triangle with side lengths , , . The formula is , where  (semi - perimeter).

2. Area - Height Relationship: The area of a triangle can also be expressed as . To find the height  corresponding to base , we use the formula .

 

Step-by-Step Solution  

1. Calculate the semi - perimeter :