The sides of a triangle are in the ratio 3, 4, 5. State whether the triangle is right angled or not.
Question
2 Answer

1. User Answers 12651241
Answer:
If the sides of a triangle are in the ratio 3:4:5, prove that it is a rightangled triangle.
Stepbystep explanation:
In order to prove that the triangle is a rightangled triangle or not, take the ratio as the length of the sides then consider the triangle to be a rightangled triangle, then prove the Pythagoras theorem. If the sides satisfy the Pythagoras theorem, then it’s a rightangled triangle otherwise, it’s not a rightangled triangle.
We are given the sides of a triangle whose ratio is 3:4:5.
Considering the sides to be 3x,4x,5x.
Since, we know that the length of hypotenuse is always greater than the other two sides, so we are taking the hypotenuse to be 5x and other remaining sides to be 3x and 4x.
We are only considering that the given triangle is a rightangled triangle. For that we need to prove that the sides follow Pythagoras theorem.
So, for Pythagora's theorem, we know that the sum of the square of the base side and square of the height side is equal to the square of the hypotenuse.
Squaring the base side 4x, we get:
(4x)2=16x2 …….(1)
Similarly, squaring the height side 3x, we get:
(3x)2=9x2 …….(2)
Squaring the hypotenuse side 5x, and we get:
(5x)2=25x2 …….(3)
Taking the sum of (1) and (2):
16x2+9x2=25x2, which is equal to the equation (3).
That means the sum of the square of base and the square of height is equal to the square of hypotenuse, that satisfies the Pythagoras theorem, that implies the triangle ABC is actually a rightangled triangle, which is rightangled at B. And this proves our consideration to be true.

2. User Answers wegnerkolmp2741o
Answer:
it is a right triangle
Stepbystep explanation:
If the triangle is a right triangle, it will meet the Pythagorean theorem
a^2 + b^2 = c^2
3^2+4^2 = 5^2
9+16=25
25=25
This is true so it is a right triangle