Question
In ∆ABC , G is the centroid , AB = 20 cm, BC= 24 cm
and AC = 28 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 202 + 282 = 2{AD 2 + (24/2) 2 } or 400 + 784 = 2{AD 2 + 144} or 1184/2 = AD 2 + 144 or 592 = AD 2 + 144 or AD 2 = 592 – 144 = 448 or AD = √448 = 8√7 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 8√7 = 8√7 /3cm
‘A’ and ‘B’ started a business by investing Rs. ‘b’ and Rs. ‘b + 400’, respectively. If 9 months later the ratio of profit shares of ‘...
A and B started a business. After 3 years they received Rs 1245 as profit in which A's share is Rs 720, then find the ratio of investment of A and B.
A and B together start a business with investment of Rs. 1500 and Rs. (x + 500), respectively. If the profit earned after 5 years is Rs. 5000 and share ...
- Akash and Bhanu started a business with initial investments of Rs. 1,200 and Rs. 2,000 respectively. After one year, Akash increased his investment by Rs. ...
Ashish started a business by investing Rs. 7,00. Few months later; Ramesh joined him by investing Rs. 8,00 such that at the end of the year, the profit ...
- 'A' invested Rs. 9,000 in a business. After 5 months, 'A' reduced the investment by Rs. 2,000 and 'B' joined with Rs. 12,000. At the end of 20 months from ...
Out of their respective monthly salaries, Soma spends 7/8 and Tina spends 4/5 on various expenses. The salary remaining with Tina after the expenses is ...
Aman, Baman and Chaman started a business with investments of 10000, 1500 and 2000 respectively. After 9 months from start of the business , Baman and C...
P started a business investing Rs.20000. After 4 months, Q joined her with the capital of Rs.25000. After another 6 months, R joined them with the capit...
'Asmita,' 'Bikshu,' and 'Chetna' jointly invested Rs. 12000, Rs. 20000, and Rs. 15000 in a construction business. After 8 months, 'Asmita' withdrew Rs. ...
Relevant for Exams:
