In triangle PQR, length of the side QR is less than twice the length of the side PQ by 3 cm. Length of the side PR exceeds the length of the side PQ by 14 cm. The perimeter is 55 cm. The length of the smallest side of the triangle PQR is:

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  1. 10 cm
  2. 11 cm
  3. 12 cm
  4. 14 cm

Answer (Detailed Solution Below)

Option 2 : 11 cm
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Detailed Solution

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Given:

Let the sides of triangle PQR be:

  • PQ = x (since we need to find the smallest side)
  • QR = 2x - 3 (QR is less than twice PQ by 3 cm)
  • PR = x + 14 (PR exceeds PQ by 14 cm)

The perimeter of the triangle is given as 55 cm.

Formula used:

Perimeter of a triangle = sum of all sides

So, x + (2x - 3) + (x + 14) = 55

Calculation:

Simplify the equation:

⇒ x + 2x - 3 + x + 14 = 55

⇒ 4x + 11 = 55

Subtract 11 from both sides:

⇒ 4x = 44

Divide by 4:

⇒ x = 11

Step 4: The smallest side is PQ = x = 11 cm.

∴ The length of the smallest side is 11 cm.

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