Question 12 of 16beginner💡 UnderstandShort Answer2 marks

Is the hypotenuse the longest side of a right triangle? Justify your answer.

Correct Answer

Yes, the hypotenuse is always the longest side of a right triangle.

Justification: By Baudhāyana's Theorem: c² = a² + b² c is the hypotenuse, and a, b are the other two sides. Since c² equals the sum of a² and b², and both a² and b² are positive: c² > a² and c² > b² Taking square roots (all lengths are positive): c > a and c > b ∴ The hypotenuse is longer than each of the other two sides.

Exercise: Figure it Out (Section 4) | Q: 4 | (Page Page 21)
For More Understanding

Explanation

The chapter establishes Baudhāyana's Theorem as a fundamental relationship in right triangles. The mathematical justification comes directly from the equation c² = a² + b². Since squares of positive numbers are always positive, and c² equals the sum of two positive quantities a² and b², it follows that c² must be greater than either a² or b² individually. This proves that the hypotenuse is the longest side.

Solution Steps

  1. State Baudhāyana's Theorem: c² = a² + b², where c is the hypotenuse

  2. Note that c² equals the sum of a² and b², both positive values

  3. Conclude that c² > a² and c² > b²

  4. Take square roots to obtain c > a and c > b

  5. Therefore, the hypotenuse is the longest side of a right triangle

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