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.

$$\Rightarrow$$ BD = CD = 3 cm

From $$\triangle$$ABD

AD$$^2$$ + BD$$^2$$ = AB$$^2$$

$$\Rightarrow$$ 4$$^2$$ + 3$$^2$$ = AB$$^2$$

$$\Rightarrow$$ 16 + 9 = AB$$^2$$

$$\Rightarrow$$ AB$$^2$$ = 25

$$\Rightarrow$$ AB = 5 cm

Hence, the correct answer is Option C

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