Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reasons.
No.
Step 1: Recall the Pythagoras theorem. It says that in a right-angled triangle,
\(\text{(Hypotenuse)}^2 = (\text{Base})^2 + (\text{Height})^2\).
Step 2: Identify the largest side, because the largest side is always taken as the hypotenuse in the Pythagoras theorem.
Here, the largest side = 25 cm.
Step 3: Now check if
\(25^2 = 24^2 + 5^2\)
Step 4: Calculate each square.
\(25^2 = 25 \times 25 = 625\)
\(24^2 = 24 \times 24 = 576\)
\(5^2 = 5 \times 5 = 25\)
Step 5: Add the squares of the smaller two sides.
\(24^2 + 5^2 = 576 + 25 = 601\)
Step 6: Compare the two values.
Left side = \(25^2 = 625\)
Right side = \(24^2 + 5^2 = 601\)
Since 625 ≠ 601, the Pythagoras theorem is not satisfied.
Final Conclusion: Therefore, the given triangle is not a right triangle.