TJ W. answered • 02/22/18
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I will solve for consecutive integers. The process for solving for consecutive even will be very similar. Let's define the three sides of the triangle from largest to smallest by using equations. We will have the smallest side be equal to "n," an integer.
c=n+2
b=n+1
a=n
Now, let's substitute these three equations into the Pythagorean Theorem, or a2+b2=c2
(n+2)2=n2+(n+1)2
Now, we can solve for "n" by FOILing out each squared factor and simplifying.
n2+4n+4=n2+n2+2n+1 <-- I foiled each squared term
n2+4n+4=2n2+2n+1 <-- Combined Like Terms
Now, let's move all of the terms onto one side to set it equal to 0.
n2-2n+-3=0
This equation factors to (n-3)(n+1)=0, giving us n=3 or n=-1
Obviously, a triangle cannot have a side of -1, so we will take n=3, giving us the three sides of the triangle as:
c=5
b=4
a=3
You can check these by plugging them into the Pythagorean theorem,
32+42=52
9+16=25
25=25 <-- This is true, so our answer is correct.
TJ W.
Right, I solved it by doing consecutive integers so as not to give the answer away.
Think about how I set up my initial equations.
If consecutive integers are n, n+1, and n+2, what would EVEN consecutive integers be?
TRY IT FIRST BEFORE READING
We can write them as a=n, b=n+2, and c=n+4. Repeat the steps I did above with these new equations, and it will give you three consecutive integers.
As a further exercise, see how those relate to the answers I came up with for consecutive integers.
HINT: they should be a multiple of the ones that I came up with.
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02/22/18
David W.
02/22/18