How do you determine if the lengths #sqrt65, 6sqrt2, sqrt97# form a right triangle?

Question

Eva Adamson · Accepted Answer

#137 !=97#

This is not a right-angled triangle.

The theorem of Pythagoras only holds true in a right-angled triangle. Test to see whether #color(red)(a^2 +b^2) = color(blue)(c^2)# is true. #color(red)((sqrt65)^2 + (6sqrt2)^2)color(white)(..........)color(blue) ((sqrt97)^2)# #color(red)(=65+36xx2)color(white)(................)color(blue) (=97)# #color(red)(=65+72)# #color(red)(=137)#

Isaiah Anthony · Answer

undefined To determine if the lengths sqrt65, 6sqrt2, sqrt97 form a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, if sqrt65, 6sqrt2, and sqrt97 form a right triangle, then the following equation should hold true:

(sqrt65)^2 + (6sqrt2)^2 = (sqrt97)^2

Simplifying the equation, we get:

65 + 72 = 97

This equation is not true, as 65 + 72 is not equal to 97. Therefore, the lengths sqrt65, 6sqrt2, and sqrt97 do not form a right triangle.