Mathematics
If the lengths of two sides of an isosceles triangle are 3 cm and 7 cm, then what is the length of the third side?
Triangles
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Answer
In an isosceles triangle, two sides are equal. The third side must be either 3 cm or 7 cm.
Case 1: If the sides are 3 cm, 3 cm and 7 cm.
Sum of two smaller sides = 3 cm + 3 cm = 6 cm
Since 6 cm < 7 cm, the triangle inequality (sum of two sides must be greater than the third side) is violated.
∴ Triangle cannot be formed.
Case 2: If the sides are 7 cm, 7 cm and 3 cm.
Sum of any two sides:
7 + 7 = 14 > 3 ✓
7 + 3 = 10 > 7 ✓
The triangle inequality is satisfied.
∴ Triangle can be formed.
Hence, the length of the third side is 7 cm.
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