ABC is an equilateral triangle with side 24 cm and AD is the median. If G is the centroid of the triangle ABC, find the length (in cm) of GD.
4\(\sqrt3\)
Median of an equilateral triangle with side a: \(\dfrac{\sqrt3}{2}a\). With a=24: \(\dfrac{\sqrt3}{2}\times24 = 12\sqrt3\) cm.
The centroid divides the median in the ratio 2:1 from the vertex, so GD (from centroid to the base) is one-third of the median: \(\dfrac{12\sqrt3}{3} = 4\sqrt3\) cm.
Hence, the length of GD is \(4\sqrt3\) cm.
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:
- 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.
- The perimeter of an equilateral triangle is $36\sqrt{3}$ m. Find the height (in metres).
- Write a Pythagorean triplet whose smallest member is 8.
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?
