To find: the altitude of the equilateral
Answer to Problem 6ST1
Explanation of Solution
Given:
The length of each side of the equilateral triangle is 12.
Concept Used:
Theorem 4-4: RHS rule states that the right triangles are congruent if any of side and hypotenuse of right triangles are congruent.
Theorem 8-7: In a
First draw an equilateral triangle as mentioned in the question:
Here
Consider the right triangles
So, by HL-theorem
Thus,
Now consider,
Apply theorem 3-11 on the triangle
Thus, the triangle
Now, by theorem 8-7, the hypotenuse is two times as long as the shorter side, so
Also, by theorem 8-7, the longer side is
Thus,
So, the length of the altitude of the given triangle is
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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