True or false? for a triangle with sides having lengths r, s, and t if r2 = s2 + t2 then the triangle must be?

Question

a right triangle

Answer 1

True. That would be true if and only if r is the longest side (hypotaneuse).

r^2 = s^2 + t^2

Answer 2

True.

Answer 3

Assuming the 2 after each variable is meant to represent squared, then yes, it is true.

If r^2 = s^2 + t^2, then the triangle must be right angled with r as the hypotenuse.

This can be seen using the cosine law.

The cosine law states:

a^2 = b^2 + c^2 - 2bc cos X

In this a is the side opposite angle X, and b and c are the two other sides (doesn't matter which order)

If a^2 = b^2 + c^2, then

2bc cos X = 0

Now either b = 0, or c = 0 (but then it wouldn't be a triangle...), or

cos X = 0

So taking the inverse cosine of both sides:

X = acos X = 90

So angle X is 90 degrees, and the triangle must be right angled.

Answer 4

is that r to the power of 2 i.e squared? if so true its a right angled triangle

Answer 5

If by r2,etc you mean r-squared (can be typed: r^2), then you are correct.  It must be a right triangle if the sum of the squares of two sides equals the square of the third side.  This was proved by Pythagoras, who had many other issues, but was a fine mathematician and geometer.

Answer 6

true.

r will be the hypotenuse side of the triangle.

by using pythagoras theorem.

longest side square is equal to the square of sum of other two sides indivdualy.