Which of these cannot represent the lengths of the sides of a right triangle?
a. 3ft, 4ft, 5ft
b. 6in, 8in, 10in
c. 16cm, 63cm, 65cm
d. 8m, 9m, 10m

Explanation:

If a = 8 and b = 9 are the two legs of a triangle and c = 10 is the hypotenuse, then

a^2 + b^2 = c^2

8^2 + 9^2 = 10^2

64 + 81 = 100

145 = 100

We get a false equation as 145 and 100 are two different values. So the original equation is false when (a,b,c) = (8,9,10)

By the converse of the pythagorean theorem, we have proven that this particular triangle is not a right triangle

Contrast this with something like choice A where we have a = 3, b = 4, c = 5 leading to

a^2 + b^2 = c^2

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

we get a true equation so a triangle with sides 3,4,5 is a right triangle. Choices B and C follow a similar path.

b) well because you get well