Question 73

The base and altitude of an isosceles triangle are 10 cm and 12 cm respectively. Then the length of each equal side is:

Solution

In the isosceles triangle, the altitude bisects the base as shown above.

Let the length of equal sides = a

From $$\triangle$$ABD,

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

$$\Rightarrow$$ 5$$^2$$ + 12$$^2$$ = a$$^2$$

$$\Rightarrow$$ 25 + 144 = a$$^2$$

$$\Rightarrow$$ a$$^2$$ = 169

$$\Rightarrow$$ a = 13 cm

$$\therefore\ $$Length of each equal side = 13 cm

Hence, the correct answer is Option A

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