Math Problem Statement

Can side d be the base for this triangle? If so, which length would be the corresponding height? If not, explain why not.

Solution

In the diagram, the question asks if side dd can be the base of the triangle. If side dd is the base, the corresponding height must be a perpendicular distance from the opposite vertex to the line containing side dd.

Looking at the diagram:

  • Side dd 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 gg, which is perpendicular to side dd, indicating that gg is the height when dd is taken as the base.

Thus, yes, side dd can be the base, and the corresponding height would be the length gg, which is the perpendicular distance from the opposite vertex to the line containing dd.

Would you like more details, or do you have any further questions?

Here are some related questions you might consider:

  1. What is the significance of choosing different sides as the base in a triangle?
  2. How do you calculate the area of a triangle using different bases and heights?
  3. Why is it important that the height be perpendicular to the base?
  4. How would the height change if side ee or side ff were chosen as the base instead of dd?
  5. 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 Area=12×Base×Height\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}, 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