Question 137
ABC is an isosceles triangle such that AB = AC = 30 cm and BC = 48 cm. AD is a median to base BC. What is the length (in cm) of AD?
Solution
Given : AB = AC = 30 cm and BC = 48 cm. AD is a median to base BC
To find : AD = ?
Solution : In an isosceles triangle, median is perpendicular to the base.
=> CD = $$\frac{48}{2}=24$$ cm
Thus, in right $$\triangle$$ ADC,
=> $$(AD)^2=(AC)^2-(CD)^2$$
=> $$(AD)^2=(30)^2-(24)^2$$
=> $$(AD)^2=900-576=324$$
=> $$AD=\sqrt{324}=18$$ cm
=> Ans - (A)
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