Triangle ABC has perimeter 22cm. AB = 8cm BC = 5cm By calculation, deduce whether triangle ABC is a right-angled triangle.

Question

asked Aug 26, 2021 25.3k views

1 Answer

Jimmy Van Beele · Answer 1 · 2021-08-30T21:53:29+0000

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.