Math Problem Statement
Solution
In the diagram, the question asks if side can be the base of the triangle. If side is the base, the corresponding height must be a perpendicular distance from the opposite vertex to the line containing side .
Looking at the diagram:
- Side is slanted, and the height must be perpendicular to this side if it is chosen as the base.
- There is a vertical dashed line labeled , which is perpendicular to side , indicating that is the height when is taken as the base.
Thus, yes, side can be the base, and the corresponding height would be the length , which is the perpendicular distance from the opposite vertex to the line containing .
Would you like more details, or do you have any further questions?
Here are some related questions you might consider:
- What is the significance of choosing different sides as the base in a triangle?
- How do you calculate the area of a triangle using different bases and heights?
- Why is it important that the height be perpendicular to the base?
- How would the height change if side or side were chosen as the base instead of ?
- Can any side of a triangle be chosen as the base, and how does that affect calculations?
Tip: The area of a triangle is always calculated using the formula , where the height must always be perpendicular to the base!
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangles
Perpendiculars
Formulas
Area of a triangle: Area = (1/2) * base * height
Theorems
Triangle area formula
Properties of perpendicular heights
Suitable Grade Level
Grades 6-8