NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Problems and Solutions
Question 22

Question. 22

Perimeter of an isosceles triangle is 50 cm. If one of the two equal sides is 18 cm, find the third side.

Answer:

Third side of the triangle = 14 cm

Detailed Answer with Explanation:

Step-by-step solution

  1. Given: The triangle is isosceles, so it has two equal sides.

    Perimeter = 50 cm

    Each equal side = 18 cm

  2. Recall the formula for perimeter of a triangle:

    \( \, \text{Perimeter} = \text{side}_1 + \text{side}_2 + \text{side}_3 \, \)

    Here: \( \, \text{Perimeter} = 18 + 18 + \text{base} \, \)

  3. Add the two equal sides:

    \( \, 18 + 18 = 36 \, \)

  4. Set up the equation using the given perimeter:

    \( \, 50 = 36 + \text{base} \, \)

  5. Solve for the base (third side):

    \( \, \text{base} = 50 - 36 \, \)

    \( \, \text{base} = 14\ \text{cm} \, \)

  6. Quick check:

    \( \, 18 + 18 + 14 = 50\ \text{cm} \, \) ✔️

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