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
More Geometry Questions
Evaluate: 360 ÷ [ {18 − (6×2)} × 5 ] + 72 − 33
(43)² - (28)² + (32)² = ?% of 2500
Evaluate:
√729 + √49 - √16 + 1/√64
What will come in place of (?) in the given expression.
12.5 + 7.75 - 3.6 = ?62 of 8 - 320 ÷ 4 = ?3 + 200
2(1/3) + 2(5/6) – 1(1/2) = ? – 6(1/6)
What will come in the place of question mark (?) in the given expression?
30% of 520 + 16% of 1500 = ? + 244
60% of 120 – ?% of 64 = 20% of 200
35% of 840 + 162 = ? – 25% × 300
20% of 240 + 18% of 200 = ?
Relevant for Exams:
