Question

Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle Not a Right Triangle 10.5 cm, 20.8 cm, 23.3 cm6 cm, 22.9 cm, 20.1 cm

Answer 1

• Right Triangle-10.5 cm, 20.8 cm, 23.3 cm
• Not a Right Triangle-6 cm, 22.9 cm, 20.1 cm

Explanation:

Given the sets of side lengths of a triangle:

• 10.5 cm, 20.8 cm, 23.3 cm

• 6 cm, 22.9 cm, 20.1 cm

To verify whether each set of side lengths could be the sides of a right triangle, we use the Pythagorean Theorem. Note that the longest side is always taken as the hypotenuse.

• Pythagoras Theorem:
  `Hypotenuse^2=Opposite^2+Adjacent^2`

In the set of side lengths 10.5 cm, 20.8 cm, 23.3 cm

`23.3^2=20.8^2+10.5^2\\542.89=432.64+110.25\\542.89=542.89`

Clearly these satisfies the required theorem and thus are side lengths of a right triangle.

In the set of side lengths 6 cm, 22.9 cm, 20.1 cm

`22.9^2=20.1^2+6^2\\524.41\\eq 440.01`

Clearly these does not satisfy the required theorem and thus are not side lengths of a right triangle.