Final answer:
The value of a, representing the height of the equilateral triangle with a perimeter of 60 inches, is 10√3 inches.
Step-by-step explanation:
Calculating the Height of an Equilateral Triangle
To find the value of a, which represents the height of the equilateral triangle, we can use the Pythagorean theorem on the 30-60-90 right triangle formed by cutting the equilateral triangle in half.
The equation becomes: a² + (½ × side length)² = (side length)². Given a perimeter of 60 inches, each side length is 20 inches. So, we have a² + (10)² = (20)², which simplifies to a² + 100 = 400.
After subtracting 100 from both sides, we find a² = 300. Taking the square root of both sides gives us a = √300 = 10√3 inches.