A triangle has sides of length 14.1 cm, 14.8 cm and 19.5 cm - OCR - GCSE Maths - Question 18 - 2020 - Paper 1

To determine if a triangle is a right-angled triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the lengths of the other two sides.

1. Identify the sides: The given sides are 14.1 cm, 14.8 cm, and 19.5 cm. The longest side is 19.5 cm.

2. Apply the Pythagorean theorem: We need to check if the following holds true:

   $(19.5)^2 = (14.1)^2 + (14.8)^2$

3. Calculate the squares:

   • $(19.5)^2 = 380.25$
   • $(14.1)^2 = 198.81$
   • $(14.8)^2 = 219.04$

4. Sum the squares of the other two sides:

   $198.81 + 219.04 = 417.85$

5. Comparison:

   Since $380.25 \neq 417.85$, it follows that:

   Therefore, the triangle with sides 14.1 cm, 14.8 cm, and 19.5 cm is not a right-angled triangle.