Question
In △ABC with centroid G and median AM, AG = 16 cm, AC
= 25 cm and ∠AMC = 90°. Find the area (in sq.cm) of △ABC.Solution
ATQ,
Given: AG = 16 cm (AG is 2/3 of median AM) So, AM = 16 × (3/2) = 24 cm AC = 25 cm, ∠AMC = 90° ⇒ use Pythagoras In △AMC: AM² + MC² = AC² 24² + MC² = 25² ⇒ 576 + MC² = 625 MC² = 49 ⇒ MC = 7 cm Area of △AMC = (1/2) × 24 × 7 = 84 cm² Area of △ABC = 2 × 84 = 168 cm²
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