Question: Which of the following triangles has the largest area given the same base?
Options:
Equilateral triangle
Isosceles triangle
Scalene triangle
Right triangle
Correct Answer: Equilateral triangle
Solution:
For a given base, an equilateral triangle has the maximum area compared to other types of triangles.
Which of the following triangles has the largest area given the same base?
Practice Questions
Q1
Which of the following triangles has the largest area given the same base?
Equilateral triangle
Isosceles triangle
Scalene triangle
Right triangle
Questions & Step-by-Step Solutions
Which of the following triangles has the largest area given the same base?
Step 1: Understand that the area of a triangle can be calculated using the formula: Area = 1/2 * base * height.
Step 2: Recognize that for triangles with the same base, the height is the key factor that affects the area.
Step 3: Know that an equilateral triangle has all sides equal and all angles equal, which allows it to reach the maximum height for a given base.
Step 4: Compare the height of an equilateral triangle to other types of triangles (like isosceles or scalene) with the same base. The equilateral triangle will always have the highest height.
Step 5: Conclude that since the equilateral triangle has the maximum height for a given base, it also has the largest area compared to other triangles.
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