The perimeter of an equilateral triangle is624 centimeters. The height of this triangle isk 3 centimeters, where k is a constant. What is thevalue of k?
Question
The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k 3 centimeters, where k is a constant. What is the value of k?
Solution
The perimeter of an equilateral triangle is equal to three times the length of one side. So, if the perimeter is 624 centimeters, then each side of the triangle (let's call it 'a') is 624/3 = 208 centimeters.
The height (h) of an equilateral triangle can be found using the formula: h = √3/2 * a.
So, in this case, the height of the triangle is k*3 centimeters, where k is a constant.
We can set up the equation √3/2 * a = k*3 to solve for k.
Substituting the value of 'a' we found earlier (208 cm), we get √3/2 * 208 = k*3.
Solving for k, we get k = (√3/2 * 208) / 3 = 60√3.
So, the value of k is 60√3.
Similar Questions
The perimeter of an equilateral triangle is624 centimeters. The height of this triangle isk 3 centimeters, where k is a constant. What is thevalue of k?
the lingths of the side of a triangle are in the ratio 3:5:6. the primiter of the triangle is 21cm find the lingth of each side on the triangle
If the perimeter of an equilateral triangle is 60 cm, then what is its area? a. 200√2cm2 b. 100√2cm2 c. 100√3cm2 d. 200√3cm2
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle
The base and height of triangle are in the ratio 3:4. If it’s area is216 cm2 . Find its base and height.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.