In an equilateral triangle with side ‘a’, find the percentage of altitude with respect to its area.
Question
In an equilateral triangle with side ‘a’, find the percentage of altitude with respect to its area.
Solution
Sure, let's solve this step by step.
Step 1: First, we need to find the altitude of the equilateral triangle. The formula for the altitude (h) of an equilateral triangle with side 'a' is h = √3/2 * a.
Step 2: Next, we calculate the area of the equilateral triangle. The formula for the area (A) of an equilateral triangle with side 'a' is A = √3/4 * a².
Step 3: Now, we need to find the percentage of the altitude with respect to the area. The formula for this is (h/A) * 100%.
Step 4: Substitute the values of h and A from steps 1 and 2 into the formula in step 3.
So, the percentage of the altitude with respect to its area is (√3/2 * a / √3/4 * a²) * 100%.
Step 5: Simplify the above expression to get the final answer.
Note: The above expression simplifies to 2/a * 100%, which means the percentage of the altitude with respect to its area is inversely proportional to the side length 'a'.
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