Geometry

Question Analysis

Given the side lengths , ,  of triangle , the task is to find the height  corresponding to side . We'll first use Heron's formula to calculate the area of the triangle and then use the area - height relationship to determine .

 

Key Concept Explanation

1. Heron's Formula: For a triangle with side lengths , , , the area , 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 :

2. Apply Heron's formula to find the area :

Click "Show Answer" to reveal the answer and analysis