G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
8 cm
The correct answer is 8 cm.
This matches our calculated AG length. $r = \frac{8\sqrt{3}}{2\sqrt{3}} = 4$ cm. The median length AD = AG + GD = R + r = 8 + 4 = 12 cm, which also matches our earlier calculation for the median length. This confirms our calculation that the length of AG is 8 cm.
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Observe the given figure and find the value of S.

In a triangle, if the angles are in the ratio 1 ∶ 2 ∶ 3, then the ratio of the corresponding sides is:
In ΔTAP, ∠TAP = 60°, TA = 6 cm, AP = 8 cm. K is the midpoint of AP. A line from K is produced to meet TP at O such that ∠AKO = 120°. Find the length of OK.
Given that Δ MAN and Δ CPT are congruent to each other such that ∠M = 75, ∠N = 65, ∠A = 40, ∠C = x/2, ∠P = 6y + 16. Find the value of (x – 5y).
If M is the mid-point of the side BC of ABC, and the area of ABM is 19 cm2 , then the area of ABC is:
In Δ PQR, S and T are points on the sides PQ and PR, respectively, such that Δ PST is similar to Δ PRQ. If m ∠PQR = 47°, then find m ∠STR.
If Δ ABC ~ ΔDEF, ∠A = 47°, and ∠E = 63°, then what is the measure of ∠C?
It is given that ΔABC ∼ ΔYZX and Ar ΔABC : Ar ΔXYZ = 256 : 25. If AB = 12 cm, BC = 10 cm, CA = 15 cm, then what is the value of YZ (in cm)?
In trapezium ABCD, AB∥DC. The sides AD and BC are produced to meet at E. AB = 15 cm, CD = 10 cm, AD = 4 cm and BC = 5 cm, then DE = ?
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:
In an equilateral triangles ABC if AD ⊥ BC, then which of the following statement is true?