In an equilateral triangle with side ‘a’, find the percentage of altitude with respect to its area.

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'.