How do you determine if the lengths #18, 24, 30# form a right triangle?

Question

Genesis Allen · Accepted Answer

see below

we use Pythagoras' theorem if #c# is the hypotenuse ( the longest side), #a " & "b" "#are the other two sides then #c^2=a^2+b^2# we ahve #30^2=900# #18^2=324# #24^2=576# #324+576=900=30^2# #:. 18,24,30" "#do form a right angle triangle

Eva Abramson · Answer

undefined To determine if the lengths 18, 24, 30 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 (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have the lengths 18, 24, and 30. We can check if the Pythagorean theorem holds true by calculating the squares of these lengths.

18^2 = 324
24^2 = 576
30^2 = 900

Now, we need to check if the sum of the squares of the two shorter sides (324 + 576) is equal to the square of the longest side (900).

324 + 576 = 900

Since the sum of the squares of the two shorter sides is equal to the square of the longest side, we can conclude that the lengths 18, 24, and 30 form a right triangle.