ABC is an isosceles triangle such that AB AC 30 cm and BC 48 cm AD is a median to base BC What is th...........

Quantitative Aptitude (CPO) Mensuration 2D

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?

- In an isosceles triangle ABC with AB = AC, the median AD to the base BC bisects BC into two equal parts.

- Given: AB = AC = 30 cm and BC = 48 cm, hence BD = DC = 24 cm.

- To find AD, we use the Pythagorean theorem in triangle ABD.

- Using the Pythagorean theorem: \(AD^2 + BD^2 = AB^2\).

- Substituting the values: \(AD^2 + 24^2 = 30^2\).

- Calculating gives: \(AD^2 + 576 = 900\).

- Simplify to find \(AD^2 = 324\), hence, AD = 18 cm.

- Option 1: 18 is the correct answer.

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