emailsimonwatts2012 emailsimonwatts2012
  • 13-03-2020
  • Mathematics
contestada

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

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bhuvna789456
bhuvna789456 bhuvna789456
  • 17-03-2020

ΔABC is not a right angled triangle.

Step-by-step 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.

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