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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