Question 188

G is the centroid of ΔABC. The medians AD and BE intersect at right angles. If the lengths of AD and BE are 9 cm and 12 cm respectively: then the length of AB (in cm) is

Solution

Given : AD = 9 & BE = 12 are medians. G is centroid of $$\triangle$$ABC

$$\angle$$AGB = 90

To find : AB = ?

Solution : A centroid divides a median in the ratio = 2 : 1

=> AG : GD = 2 : 1

=> AG = 6 cm

Similarly, BG = 8 cm

Now, in right angled $$\triangle$$ABC

=> AB = $$\sqrt{(AG)^2 + (BG)^2}$$

=> AB = $$\sqrt{6^2 + 8^2} = \sqrt{100}$$

=> AB = 10 cm

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