Question

Triangle ABC has perimeter 22cm.

AB = 8cm
BC = 5cm
By calculation, deduce whether triangle ABC is a right-angled triangle.

Answer 1

ΔABC is not a right angled triangle.

Explanation:

• Step 1: Given the perimeter of ΔABC = 22 cm, sides AB = 8 cm and BC = 5 cm. Find the side AC.

Perimeter = AB + BC + AC

⇒ AC = 22 - (8 + 5) = 22 - 13 = 9 cm

• Step 2: Find whether the triangle is right angled using Pythagoras Theorem which is Hypotenuse² = Side² + Base²

AC² = AB² + BC²

⇒ AC² = 9² = 81

⇒ AB² + BC² = 8² + 5² = 64 + 25 = 89

∴ AC² ≠ AB² + BC²

⇒ ΔABC is not a right angled triangle.