Question 70
In the given figure, $$\triangle$$ABC is an isosceles triangle, in which AB = AC, AD $$\perp$$ BC, BC = 6 cm and AD = 4 cm. The length of AB is:
Solution
Given, $$\triangle$$ABC is an isosceles triangle
AB = AC
The perpendicular from A to BC will bisect the side BC.
$$\Rightarrow$$Â BD = CD = 3 cm
From $$\triangle$$ABD
AD$$^2$$ + BD$$^2$$ = AB$$^2$$
$$\Rightarrow$$Â 4$$^2$$ + 3$$^2$$ = AB$$^2$$
$$\Rightarrow$$Â 16 + 9 = AB$$^2$$
$$\Rightarrow$$Â AB$$^2$$ = 25
$$\Rightarrow$$ Â AB = 5 cm
Hence, the correct answer is Option C
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