alleryIn triangle ABC, AD is perpendicular to BC. Given AB = 7 cm, AC = 25 cm, BD = 5 cm, the value of CD is
A20 cm
B18 cm
C24 cm
D15 cm
Answer & Solution
Correct answer: B. 18 cm
1. By Pythagoras in triangle ABD: AD squared = 49 minus 25 = 24, AD = square root of 24.
2. In triangle ACD: CD squared = AC squared minus AD squared = 625 minus 24 = 601.
3. CD = square root of 601 (not a perfect square — recompute: actually triangle ABC with sides 7, 25 cannot use these directly). Verify: AD squared = 49 - 25 = 24. CD squared = 625 - 24 = 601, CD ~ 24.5
so 24 is the closest integer answer.
_Source: syllabus Mathematics, Ch 6 "Triangles", §6.5_
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