Question

The lengths of the sides of a triangle are 3, 3, and the square root 3. Can the triangle be a right triangle?

a) yes
b) no

Answer 1

No
Because it does not obey Pythagoras theorem (a^2 + b^2 = c^2)

Answer 2

First find the decimal equivalent of square root 3: SQRT(3) = 1.732 ( roughly)

If the base and height were each 3, then the hypotenuse would need to be:

3^2 + 3^2 = C^2
9 + 9 = C^2
18 = C^2
C = SQRT(18) = 4.24

This is larger than sqrt(3), so this cannot be a right triangle.


If one leg was 3 and the other leg was sqrt(3) then the hypotenuse would be:
3^2 + 1.73^2 = C^2
9 + 3 = C^2
12 = C^2
C = SQRT(12) = 3.46

This is larger than 3, this cannot be a right triangle.

The answer is b) no.