If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse? First draw the right-angled triangle with these sidelengths and measure the hypotenuse, then check your answer using Baudhāyana's Theorem.
Given: Shorter sides a = 5 cm and b = 12 cm. Formula: Baudhāyana's Theorem: a² + b² = c² Substitution: 5² + 12² = c² Calculation: 25 + 144 = c² 169 = c² Answer: c = = 13 cm
Explanation
By Baudhāyana's Theorem (also known as the Pythagorean Theorem), in a right-angled triangle with sides a, b, and hypotenuse c, the relation a² + b² = c² holds. The chapter demonstrates this through the construction showing that the square on the hypotenuse equals the sum of squares on the other two sides. When drawn and measured, the hypotenuse should measure approximately 13 cm, which can be verified using the theorem.
Solution Steps
Step 1: Apply Baudhāyana's Theorem: a² + b² = c²
Step 2: Substitute the given values: 5² + 12² = c²
Step 3: Calculate: 25 + 144 = c²
Step 4: Simplify: 169 = c²
Step 5: Solve for c: c = = 13 cm