The lengths of the sides of a triangle are consecutive even integers.Find the length of the longest side if it is 14 units shorter than the perimeter

Since the sides are consecutive even integers, it has perimeter
P=x+(x+2)+(x+4)

If you are familiar with Pythagorean triangles, this alone gives away the solution.

By Pythagoras:



Solve for x. You will notice the length of the hypoteneuse is 14 shorter than the perimeter.
It works out that way.

Quote:

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Originally Posted by galactus

If you are familiar with Pythagorean triangles, this alone gives away the solution.

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Looks like we have no reason to assume that the solution is a right angle triangle and ignore that the perimeter is longer than the longest side by a certain number.
Wouldn't it be just this (here a is the shortest side)?

a + (a+2) + (a+4) = (a+4) + 14 => a = 6 and so on.

I was thinking this as well... the triangle is not necessarily a right angled triangle.

Or, if we want to go faster, we do:

Let the longest side be x.

P - 14 = x
P = (x-4) + (x-2) + x

[(x-4) + (x-2) + x] - 14 = x

Yes, my bad. False assumption.

Force of habit. I am so used to these problems involving right triangles.

Coincidentally, I had just gone over a problem that stated "one side of a right triangle is 7 units more than the short side, and the hypoteneuse is 8 more than the short side. What are the side lengths?".