Lines AB, AC, AD are pairwise perpendicular. Find the segment BD if AC = 18 dm, BC = 32 dm, BP = 10 dm.

univerkov | July 24, 2021 | education

Consider a triangle ABC (angle A = 90 °, since AB is perpendicular to AC): AC = 18 dm, BC = 32 dm.

By the Pythagorean theorem: AB = √ (BC² – AC²) = √ (32² – 18²) = √ (1024 – 324) = √700 (dm).

Consider a triangle ABD (angle A is 90 °, since AB is perpendicular to AD): AD = 10 dm, AB = √700 dm.

By the Pythagorean theorem: BD = √ (AB² + AD²) = √ ((√700) ² + 10²) = √ (700 + 100) = √800 = √ (400 * 2) = 20√2 (dm).

Answer: the BD segment is equal to 20√2dm.

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