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Q40

40Two sides of a right triangle measure 15 cm and 17 cm. Which of the following statements can be true of the length of the third side of the triangle? A. It is between 4 cm and 7 cm. E. It is between 20 cm and 23 cm. C. It is less than 10 cm.
  • Option : D
  • Explanation : In a right triangle, measure of two sides are 15 cm and 17 cm.
    Let the 3rd side of the triangle be 'x' cm
    Now, there are two cases,
    (i) (15)2 + x2 = (17)2 (as according to the pythagoras theorem)
    ⇒ 225 + x2 = 289
    ⇒ x2 = 289 - 225
    ⇒ x2 = 64
    ⇒     x = 8cm
    (ii) (15)2 + (17)2 = x2
    ⇒ 225 + 289 =x2 ⇒ x = 514
    ⇒ x = 2267cm
    So, statement B and C are true.
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