Question

12) Triangle ABC has perimeter 25 cm

AB=8.5cm BC= 6.3cm
By calculation, deduce whether triangle ABC is a right-angied

Answer 1

Hello !

Answer:

`\boxed{\sf Triangle\ ABC\ is\ not\ right-angled.}`

Explanation:

Given :

• AB=8.5cm
• BC=6.3cm
• perimeter : 25cm

The perimeter of triangle ABC is 25cm.

Moreover, this perimeter is equal to
`\sf AB+AC+CB`.

Therefore, we have
`\sf AB+AC+CB=25`

Let's replace AB and BC with their values :

`\sf 8.5+6.3+AC=25`

`\sf AC+14.8=25`

Now let's substract 14.8 from both sides :

`\sf AC=25-14.8\\\boxed{\sf AC=10.2cm}`

Furthermore, according to the Pythagorean Theorem, if the triangle is right-angled, then the square of the hypotenuse of the triangle is equal to the sum of the squares of the other two sides.

The hypotenuse is the largest side, so in this triangle, it is AC.

• 
  `\sf AC^2=10.2^2=104.04`
• 
  `\sf AB^2+BC^2=8.5^2+6.3^2=111.94`

`AC^2\\e AB^2+BC^2`

Triangle ABC is not right-angled.

Have a nice day ;)