Bissoy.com
Doctors Medicines MCQs Q&A

In the figure given below ABC is an equilateral triangle of side 6√3 cm and AD is the median of the triangle from point A and G is the centroid of the triangle. If DP = 4 cm, then what is the length of GP?

In the figure given below ABC is an equilateral triangle of side 6√3 cm and AD is the median of the triangle from point A and G is the centroid of the triangle. If DP = 4 cm, then what is the length of GP? Correct Answer 5 cm

GIVEN:

AB = BC = CA = 6√3 cm and AD is the median of the triangle and G is the centroid of the triangle. DP = 4 cm.

CONCEPT:

In equilateral triangle, all the centers (Incentre, circumcenter, orthocenter, centroid) lie at the same point, so median AD will be perpendicular to BC and it will bisect BC too.

Centroid divides the median in the ratio 2 : 1.

CALCULATION:

Now,

BD = 6√3 / 2 = 3√3 cm

Since, in equilateral triangle, all the centers lie at the same point. So, AD is perpendicular to BC.

In ∆ABD,

AB2 = BD2 + AD2

⇒ (6√3)2 = (3√3)2 + AD2

⇒ AD = 9 cm

⇒ GD = 9 × (1 / 3) = 3 cm

In ∆GDP:

GP2 = GD2 + DP2

⇒ GP2 = 32 + 42

∴ GP = 5 cm

Related Questions

Which of the following are the correct statements with regard to positive skewed distribution? (A) Mean > Media > Mode (B) Mean < Median < Mode (C) Q3 - Median < Median - Q1 (D) Q3 - Median > Median - Q1 (E) Mean = Median = Mod Choose the correct answer from the options given below:
How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of  metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is  metres to the east of point 'T'. Point 'M' is  metres to the east of point 'Z'. Point 'R' is  metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.
Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?
Point P is 4m in the west of point V. Point R is 6m in the north of point Q. Point T is 5m in the south of point S. Point V is in the middle of point R and Q. Point U is 5m in the east of point R. Point V is in north of point Q. Point S is 5m in the east of point V. What is the area of triangle formed by point P, R and Q?
Point A is 3m in the north of point B. Point D is 2m in the east of point E. Point F is 9m in the west of point G. Point C is 4m in the west of point B. Point C is 3m in the south of point D. Point F is 5m in the south of point E. Point H is 5m in the north of point G. What is the shortest distance between point H and point A?
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
In the following figure, triangle ABC is an equilateral triangle and triangle CDE is a right angled triangle. If the length of side AE is 20 units, then what will be the length of side DB?
Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. If point G is 4m to the north of Point H, then what is the distance between H and D?
Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. How far and in which direction is Point G from Point A?
The side of an equilateral triangle ABC is 28 cm. Find the side of another equilateral PQR whose area is 16 times the area of triangle ABC.