Triangle ABC has a perimeter of…

Maths Questions

Triangle ABC has a perimeter of 22 cm, with AB = 8 cm and BC = 5 cm. Based on this information, can you determine if triangle ABC is a right-angled triangle?

Answer

To determine the length of the third side of Triangle ABC, we will first add the lengths of sides AB and BC, then subtract this from the triangle’s total perimeter of 22 cm. Thus, we compute: 22 cm – (8 cm + 5 cm) = 22 cm – 13 cm = 9 cm. This remaining length represents the longest side, which we identify as the hypotenuse. We can now apply the Pythagorean Theorem to check if Triangle ABC is a right triangle, which states that a¬≤ + b¬≤ must equal c¬≤, where a and b are the two shorter sides and c is the hypotenuse. Checking our values: 8¬≤ + 5¬≤ should equal 9¬≤. Performing the calculations gives us 64 + 25 = 89, and 9¬≤ is 81. Since 89 is greater than 81, Triangle ABC does not form a right triangle; in fact, it is obtuse since the sum of the two shorter sides exceeds the length of the longest side.

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