lengths of sides of right triangle are consec. even integers

[Love21]

The lengths of the sides of a right triangle are consecutive even integers, and the length of the shortest side is x.
Which of the following equations could be used to find x?

(a) x + x + 1 = x + 2

(b) x(squared) + ( x + 1)(squared) = (x + 2) (squared)

(c) x(squared) + (x + 2)(squared) = (x + 4)(squared)

(d) x + x + 2 = x + 4

(e) x(squared) = (x + 2)(x + 4)

I have looked at this problem a dozen times and i really can't even imagine where to begin
Suggestions?
Thank you!

 

[Mrspi]

Re: I cant even begin to know...

The lengths of the sides of a right triangle are consecutive even integers, and the length of the shortest side is x.
Which of the following equations could be used to find x?

(a) x + x + 1 = x + 2

(b) x(squared) + ( x + 1)(squared) = (x + 2) (squared)

(c) x(squared) + (x + 2)(squared) = (x + 4)(squared)

(d) x + x + 2 = x + 4

(e) x(squared) = (x + 2)(x + 4)

I have looked at this problem a dozen times and i really can't even imagine where to begin
Suggestions?
Thank you!

Just one suggestion: Pythagorean Theorem

 

[Deleted member 4993]

If one even number is 'x' - then the next (consecutive) even number is 'x+2' and the next even number is ???

 

[TchrWill]

The lengths of the sides of a right triangle are consecutive even integers, and the length of the shortest side is x.
Which of the following equations could be used to find x?
(a) x + x + 1 = x + 2
(b) x(squared) + ( x + 1)(squared) = (x + 2) (squared)
(c) x(squared) + (x + 2)(squared) = (x + 4)(squared)
(d) x + x + 2 = x + 4
(e) x(squared) = (x + 2)(x + 4)

x, (x + 2) and (x + 4) combined with the Pythagorean Theorem are the two best clues given you.

You might also ask yourself if there are any Pythagorean triangles that come to mind whose sides differ by 1. Then...???