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The perimeter of a triangle is 40cm and its area is 60 cm². If the largest side measures 17cm, then the length (in cm) of the smallest side of the triangle is
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- 4
- 6
- 8
- 15
- 4
Correct Option: C
Smallest side of the triangle = x cm (let)
∴ Second side of triangle = 40 – 17 – x = 23 – x
| Semi-perimeter = s = | = 20 | |
| 2 |
∴ √s (s - a)(s - b)(s - c)
⇒ √20(20 - 17)(20 - x)(20 - 23 - x) = 60
⇒ (20 - x)(x - 3) = 60
⇒ (20 – x) (x – 3) = 60
⇒ 20x – 60 –x² + 3x = 60
⇒ x² – 23x + 120 = 0
⇒ x² – 15x – 8x + 120 = 0
⇒ x (x – 15) – 8 (x – 15) = 0
⇒ (x – 8) (x – 15) = 0
⇒ x = 8 or 15
⇒ Smallest side = 8 cm
