Question
In ∆ABC , G is the centroid , AB = 5 cm, BC= 6 cm and
AC = 7 cm , find GD, where D is the mid-point of BC?Solution
If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 5 2 + 72 = 2{AD 2 + (6/2) 2 } or 25 + 49 = 2{AD 2 + 9} or 74/2 = AD 2 + 9 or 37 = AD 2 + 9 or AD 2 = 37 – 9 = 28 or AD = √28 = 2√7 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 2√7 = 2√7 /3cm
Five years ago, the average age of a family of four members was 25 years. Six years hence, the ratio of their ages will be 9:7:5:3. Find the a...
The present ages of A and B are in the ratio 7 : 5. After 6 years, the ratio of their ages will be 4 : 3. Find A's present age.
My grandfather’s age was seven times older to me 14 years ago. He would be two times of my age seven years from now. Seven years ago, what was the...
The current average age of students in a class is 24 years. What will the average age of the students be in 6 years?
Present age of ‘A’ is 25% more than that of ‘B’. If 9 years hence from now, ‘B’ will be 6 years younger than ‘A’, then find the sum of p...
6 years from now, the ratio of ages of Amit and Sumit will be 4:5, respectively. The sum of their present ages is 114 years. What is the difference betw...
- Five years from now, the sum of the ages of ‘X’ and ‘Y’ will be 50 years. Ten years ago, ‘X’ was 8 years younger than ‘Y’. What will be the...
Five years from now, K and M together will be 80 years old. If their present ages are in the ratio 4:3, find the difference in their ages.
Five years ago, the ratio of Aman's age to Rahul's age was 6:5. It is also known that Aman's age will be 47 years five years from now. Additionally, R...
Four years ago, the ages of the father and his son were in the ratio 7:2. Four years hence, the ages of the father and his son will be in the ratio 9:4....
Relevant for Exams:
