Equilateral Triangle Properties
An equilateral triangle has three equal sides and three equal angles (each 60 degrees). The perimeter is the total length of all sides.
Calculating Side Length from Perimeter
Given the perimeter ($P$) of the equilateral triangle is $36\sqrt{3}$ m.
The formula for the perimeter is $P = 3 \times side$. Let the side length be '$s$'.
So, $3s = 36\sqrt{3}$ m.
To find the side length, divide the perimeter by 3:
$s = \frac{36\sqrt{3}}{3} = 12\sqrt{3} \text{ m}$
Finding the Height
The formula for the height ($h$) of an equilateral triangle with side length '$s$' is:
$h = \frac{\sqrt{3}}{2} \times s$
Substitute the calculated side length ($s = 12\sqrt{3}$ m) into the height formula:
$h = \frac{\sqrt{3}}{2} \times (12\sqrt{3})$
Multiply the terms:
$h = \frac{12 \times (\sqrt{3} \times \sqrt{3})}{2}$
Since $\sqrt{3} \times \sqrt{3} = 3$:
$h = \frac{12 \times 3}{2} = \frac{36}{2}$
$h = 18 \text{ m}$
Therefore, the height of the equilateral triangle is 18 metres.
Similar Questions
- In $\Delta PQR$, QR is extended up to S, so that RS = RP. If $\angle RPQ = 55^\circ$ and $\angle PRS = 110^\circ$, then find the measure of $\angle PQS$.
- In a triangle, if angle $A = 30^\circ$ and angle $B = 45^\circ$, then what is the angle of C?
- The total measure of angles in a triangle is:
- ABC is a triangle. BI and CI are angle bisectors of $\angle ABC$ and $\angle ACB$. $\angle BAC = 45^\circ$. Find the measure of $\angle BIC$.
- A side of the triangle is 15 cm and the height of the triangle from this side is 6 cm. Find the area of triangle.
- Area of an equilateral triangle is $49\sqrt{3}\text{ cm}^2$. Find the side of the triangle.
- In a triangle the ratio of angles is 2 : 3 : 4. Find the difference between the greatest and the smallest angle.
- Write a Pythagorean triplet whose smallest member is 8.
- The lengths of two sides of a triangle are 7 cm and 8 cm respectively and the measure of the angle included between these two sides is $60^\circ$. The length (in cm) of the third side of the triangle is:
- The lengths of three medians of a triangle are 3 cm, 6 cm and 5 cm. The area of the triangle is:
Important Questions from Triangles
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
In ∆ABC, 2∠A = 3∠B = 6∠C. What is the value of the largest angle among these three angles?
The longest side in a right-angled triangle is called :
The sum of two sides of a triangle with the third side is
