Question 164

ΔABC is an isosceles triangle with AB = AC = 10 cm, AD = 8 cm is the median on BC from A. The length of BC is

Solution

NOTE :- In an isosceles triangle, the median bisects at right angle.

Here, AB = AC = 10 and AD = 8

AD is perpendicular bisector.

From $$\triangle$$ABD,

BD = $$\sqrt{(AB)^2 - (AD)^2}$$

= $$\sqrt{10^2-8^2}$$ = $$\sqrt{100-64}$$

= 6

=> BC = 2*BD = 2*6 = 12 cm

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