Question

What's the answer for the attachment

Answer 1

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,

`AC^2 = AB^2+BC^2`

Substituting the values we get,

`8^2 = 7^2 + 3^2\\\\64 = 49 + 9\\\\64 \\eq 58`

Thus the pythagoras theorem is not satisfied

Thus ABC is not a right angled triangle