CDS 2026 (I) Elementary Mathematics, question 55

Topic: Geometry

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Q55

ABC is a triangle right-angled at C. Let P be the midpoint of BC. If $AP=4\sqrt{13}$ cm and $AB=20$ cm, then what is the perimeter of the triangle ABC ?

(a) 40 cm
(b) 48 cmCorrect answer
(c) 50 cm
(d) 60 cm

Solution.

Answer: (b) 48 cm

Let $AC = a$ and $BC = b$ .
Pythagoras in ABC and APC gives $a^{2} + b^{2} = 400$ and $a^{2} + b^{2}/4 = \left( 4\sqrt{13} \right)^{2} = 208$ .
Subtract: $3b^{2}/4 = 192$ , so $b = 16$ .
Then $a = 12$ , and the perimeter is $12 + 16 + 20 = 48cm$ .