Question

Triangle ABC has perimeter 20 cm.

AB = 7 cm.
BC = 4 cm.
By calculation, deduce whether triangle ABC is a right-angled triangle.

Answer 1

You have an obtuse, scalene triangle, so no :)

Explanation:

Side a = 4

Side b = 9

Side c = 7

Angle ∠A = 25.209° = 25°12'32" = 0.43998 rad

Angle ∠B = 106.602° = 106°36'6" = 1.86055 rad

Angle ∠C = 48.19° = 48°11'23" = 0.84107 rad

Answer 2

Triangle ABC is not a right-angle triangle.

Explanation:

perimeter of the triangle: 20cm

AB=7cm and BC=4cm.

We can do the third length (AC) by subtracting the known lengths from the perimeter: 20 - 7 - 4 = 9

Therefore, the length AC is 9.If

ABC were a right angle triangle, we'd be able to use Pythagoras's Theorem to work out the length AC.

AC is the hypotenuse of the triangle because it is the longest length.

a2 + b2 = c242 + 72 = 16 + 49 = 65

Where AC = c, c2 = 65 If c = 9, then c2 = 81, however when using Pythagoras, c2 = 65.

I hope this helps. I am sorry if you get this wrong.