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The perimeter of a triangle is 40 cm and its area is 60 \( \large cm^{2} \). If the largest side measures 17 cm. then the length (in cm) of the smallest side of the triangle is :

A) 4
B) 6
C) 8
D) 15
E) None of these

Correct Answer:



C) 8

Description for Correct answer:
Let the sides of the triangle = x cm and (23 - x) cm

s = \( \Large \frac{perimeter}{2} \) = \( \Large \frac{40}{2} \) = 20 cm

60 = \( \large \sqrt{s(s - 17)(s - x)(s-23 + x)} \)

60 = \( \large \sqrt{20(20-17)(20-x)(20 - 23 + x)} \)

\( \large 60^{2} \) = 20(3)(20 - x) (x - 3)

(x - 3)(20 - x) = \( \Large \frac{60^{2}}{60} \)

20x - \( \large x^{2} \) - 60 + 3x = 60

\( \large x^{2} \) - 23x + 120 = 0

(x -8) (x - 15) = 0 => x = 8, 15

Required side = 8cm

Part of solved SBI JuniorAssociate-2 questions and answers : Exams >> Bank Exams >> SBI JuniorAssociate-2

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