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Each of the two equal sides of an isosceles triangle is 3 cm longer than its base. The perimeter is 39 cm. Find the base (in cm).

Class 8Linear Equations in One VariableLinear Equations
  • A14
  • B13
  • C11
  • D15

Step-by-Step Solution

Let the base be cm, so each equal side is cm. Perimeter: → → → cm. Check: 11 + 14 + 14 = 39. The trap 14 is the length of an equal side, and 13 comes from dividing 39 by 3 as though all three sides were equal.
Answer: C) 11

Key idea: The five-step recipe

For any linear equation in one variable, follow this order:

1. **Open brackets** if any (use distributive property).
2. **Clear fractions** by multiplying both sides by the LCM of all denominators.
3. **Move all variable terms to one side**, all constants to the other (transposition — flip signs).
4. **Combine like terms** on each side.
5. **Divide** both sides by the coefficient of the variable.

Then **verify** by substituting back into the original equation. Always.

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