Question

Triangle ABC has perimeter 22 cm.

AB = 8 CM
BC = 5cm

By calculation, deduce whether triangle ABC is a right-angled triangle.

Answer 1

Triangle ABC is not a Right Triangle

Explanation:

The perimeter of a triangle is all of the sides added together so we can model our equation like so:

AB + BC + CA = P

or

8 + 5 + CA = 22

We first combine like terms

13 + CA = 22

Then make the variable have no numbers on its side

13 + CA = 22

-13 -13

CA = 9

So now that we know what CA is, we can determine whether or not its a right triangle

We can use the Pythagorean Theorem for this:

a^2 + b^2 = c^2 (the '^' symbol means 'to the power of')

or

5^2 + 8^2 = 9^2

Now we Solve

5^2 = 25

8^2 = 64

9^2 = 81

25 + 64 =? 81

89 does not equal 81

So Triangle ABC is not a Right Triangle