If I know c squared equals 49 inches, what are a squared and b squared using the Pythagorean theorum?

If you know that C^2=49 you must know either A or B to find the other.

If c^2 = 49, a^2 = 4 and b^2 = 45

If c^2 = 49, a^2 = 9 and b^2 = 40

and so on.

No. If I know c squared equals 49 square inches, then a squared must be between 0 and 49 square inches, and b squared is 49 minus a squared, which will also be between 0 and 49 square inches.

You could have a = 1, b = 6.9282...

You could have a = 2, b = 6.7082...

You could have a = 3, b = 6.3255..

You could have a = 4, b = 5.7445...

And an infinity of other possibilities

0 < a^2 < 49

0 < b^2 < 49

but there are NO specific answers given this information. If you know one, a or b, then you can calculate the other

If c² = 49, then we know the hypotenuse is √49 = 7.

You have an infinite number of choices for a and b, so long as a²+b² = c².

EXAMPLE. Let a² = 25

.....then b² = c²- a² = 49-25 = 24

.....so a = √25 ⇒ a = 5 and b = √24

EXAMPLE. Let a² = 9

.....then b² = c²-a² = 49-9 = 40

.....so a = √9 ⇒ a = 3 and b = √40

EXAMPLE. Let a² = 4

.....then b² = c²-a² = 49-4 = 45

.....so a = √4 ⇒ a = 2 and b = √45

You end up with:

a² + b² = 49

You have two unknowns with one equation which will give you an infinite number of solutions.

We would need some other piece of information that compares a to b in order to get a more specific answer.

this question makes no sense