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 $\triangle ABC$, $BD \perp AC$ at $D$ and $\angle DBC = 40^\circ$. $E$ is a point on $BC$ such that $\angle CAE = 37^\circ$. What is the measure of $\angle AEB$?
- 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:
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Important Questions from Triangles
Among the following options, which are NOT sides of a triangle?
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
In the equilateral Δ ABC, the base BC is trisected at D and E. The line through D, Parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the Δ DHE to the area of the Δ ABC?
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
A man goes 24 m towards east and then 10 m towards north. How far is he away from his initial position?
