Triangle abc has a perimeter of 22cm. ab=8cm bc=5cm bt calculation, deduce whether triangle abc is a right-angled triangle.

First let's find the length of the last side. We can do this by adding AB and BC together, then subtracting this amount from the perimeter of Triangle ABC, 22 cm.
ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)
                                    22cm - 13cm = 9cm

The hypotenuse is always the longest side of a triangle, so we know that the side we figured out is the hypotenuse. Now we can use the Pythagorean Theorem to see whether the triangle is a right triangle.

Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse.
If a² + b² do equal c², then the triangle is a right triangle.

8² + 5² = 9²
64 + 25 = 81
89 > 81

The triangle is not a right triangle, but we know that it is obtuse since a and b together are longer than c.

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