If a right-angled triangle has a short side of length 8 cm and hypotenuse of length 17 cm, what is the length of the third side? Again, try drawing the triangle and measuring, and then check your answer using Baudhāyana's Theorem.
Given: Short side = 8 cm, Hypotenuse = 17 cm
Formula: Baudhāyana's Theorem: a² + b² = c² Rearranged: b² = c² - a²
Substitution: b² = 17² - 8²
Calculation: b² = 289 - 64 b² = 225 b =
Answer: The length of the third side is 15 cm.
Explanation
Using Baudhāyana's Theorem a² + b² = c², where c is the hypotenuse, we can find the missing side. The chapter shows that this theorem applies to all right-angled triangles, not just isosceles ones. When one side and the hypotenuse are known, the other side can be found by rearranging the formula: b² = c² - a².
Solution Steps
Step 1: Apply Baudhāyana's Theorem: a² + b² = c²
Step 2: Rearrange to find the unknown side b: b² = c² - a²
Step 3: Substitute the given values: b² = 17² - 8²
Step 4: Calculate: b² = 289 - 64 = 225
Step 5: Solve for b: b = = 15 cm