The perimeter of an equilateral triangle is 360 centimeters. The height of this triangle is ksqrt (3) centimeters. What is the value of k? square

To find the value of \( k \) in the height of the equilateral triangle, we need to use the formula for the height of an equilateral triangle.<br /><br />Given:<br />- Perimeter of the equilateral triangle = 360 cm<br />- Height of the triangle = \( k\sqrt{3} \) cm<br /><br />First, we find the side length of the equilateral triangle:<br />\[ \text{Side length} = \frac{\text{Perimeter}}{3} = \frac{360}{3} = 120 \text{ cm} \]<br /><br />Next, we use the formula for the height of an equilateral triangle:<br />\[ \text{Height} = \frac{\sqrt{3}}{2} \times \text{Side length} \]<br /><br />Substitute the side length into the height formula:<br />\[ k\sqrt{3} = \frac{\sqrt{3}}{2} \times 120 \]<br /><br />Simplify the equation:<br />\[ k\sqrt{3} = 60\sqrt{3} \]<br /><br />Divide both sides by \(\sqrt{3}\):<br />\[ k = 60 \]<br /><br />Therefore, the value of \( k \) is \( \boxed{60} \).