Question
- If the area of a triangle is 24 and its base is 6, what
is the length of the altitude to that base?
is the length of the altitude to that base?
Ask by Grant Cook. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The altitude is 8 units long.
Solution
To find the length of the altitude to the base of a triangle, we can use the formula for the area of a triangle:
Given that the area of the triangle is 24 and the base is 6, we can substitute these values into the formula to solve for the altitude.
Let’s denote the altitude as
Now, we can solve for
Solve the equation by following steps:
Solve the equation by following steps:
- step0: Solve for
:
- step1: Multiply the terms:
- step2: Swap the sides:
- step3: Divide both sides:
- step4: Divide the numbers:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find the altitude of the triangle, you can use the area formula: Area = 1/2 * base * height. Plugging in the given values, we get 24 = 1/2 * 6 * height. Solving for height, we multiply both sides by 2 to get 48 = 6 * height, then divide by 6, resulting in a height of 8. So, the altitude to the base is 8 units!
Interestingly, this method really highlights how triangles carry their secrets hidden in their shapes! Elevating the concept, the altitude essentially acts as a bridge connecting the flat base to the peak, showcasing the beauty of geometry in nature and architecture alike.
