ABC is a right triangle is which angle A =90 0 , is perpendicular to BC, AB=5 cm and BD=3cm. Then CD is equal to

The question is garbled, but the intended setup is clear: in right triangle ABC with the right angle at A, AD is perpendicular to hypotenuse BC, with D on BC. Given AB = 5 cm and BD = 3 cm, find CD.

The core concept is the projection (similar triangles) property of the altitude to the hypotenuse. Triangles ABD and CBA are similar, so AB/BC = BD/AB, which gives AB² = BD × BC. Substituting, 25 = 3 × BC, so BC = 25/3 cm. Then CD = BC − BD = 25/3 − 3 = 16/3 cm. Option B is correct.

• A) 5 cm is just the length of AB. It is not CD.
• C) 25/3 cm is the full hypotenuse BC, not the segment CD.
• D) 8 cm does not follow from the data. It would need BC = 11 cm, which contradicts AB² = BD × BC.

This is a basic geometry item from the mensuration and reasoning part of CSAT. The same altitude relations, AD² = BD × DC and AB² = BD × BC, recur in many numerical questions.

Trap: Aspirants often stop at BC = 25/3 and mark C, forgetting to subtract BD.