ABC is not a right angled triangle
Solution:
Given that, Triangle ABC has perimeter 18 cm
AB = 7 cm
BC = 3 cm
We have to find whether ABC is a right angled triangle
Let the sides of triangle be AB, BC, AC
Perimeter of triangle is given by formula:
perimeter = sum of length of all three sides of triangle
18 = AB + BC + AC
18 = 7 + 3 + AC
AC = 18 - 10
AC = 8
Thus the length of sides of triangle are:
AB = 7 cm
BC = 3 cm
AC = 8 cm
For a triangle to be right angle, it must satisfy the pythagoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
The longest side of triangle is hypotenuse
Therefore, AC = 8 cm is the hypotenuse
Thus by above theorem we get,
[tex]AC^2 = AB^2+BC^2[/tex]
Substituting the values we get,
[tex]8^2 = 7^2 + 3^2\\\\64 = 49 + 9\\\\64 \neq 58[/tex]
Thus the pythagoras theorem is not satisfied
Thus ABC is not a right angled triangle
