Question

if the sides of a triangle are in the ratio 3:4:5 prove that it is right angle triangle​

Answer 1

Answer:

Given the sides are in the ratio 3:4:5.

Let ABC be the given triangle.

Let the sides be 3x,4x and hypotenuse be 5x.

According to Pythagoras theorem,

AC ^2 =BC ^2 +AB ^2

BC ^22+AB ^2=(3x) ^2 +(4x) ^2

=9x ^2+16x ^=25x ^2

AC ^2=(5x)^2 =25x ^2

AC ^2=BC ^2+AB ^2

Hence ABC is a right angled triangle.

solution

Answer 2

Step-by-step explanation:

Let, the sides of the triangle ABC be 3x, 4x and 5x.

So, AB = 3x BC = 4x AC = 5x

We know that, all traingles which follow Pythagoras theorem are right angled triangles.

So, to prove △ABC we need to prove that,

AC² = AB² + BC²

LHS = AC² = (5x)² = 25x²

RHS = AB² + BC²

= (3x)² + (4x)²

= 9x² + 16x²

= 25x²

Therefore, LHS = RHS

Thus, △ABC follows Pythagoras theorem. So, it is a right angled triangle.

Hence, proved.