The hypotenuse of a right triangle is 10 ft long. the shorter leg is 2ft shorter than the longer leg. find the side lengths of the triangle

Since we have two possible pieces of information and 2 items to solve for, we know this is a system of equations.

Our first piece of information is that our shorter leg (s) is 2 feet shorter than our longer leg (l). This can be written as s=l-2.

Our second piece of information is that using the Pythagorean theorem that our shorter leg squared plus our longer leg squared is equal to our hypotenuse squared. This can be represented by s^2+l^2=10^2. Now we can solve.

We have already isolated for s in our first equation, so we can substitute l-2 in.

(l-2) ^2+l^2=10^2

l-2+l=10

2l-2=10

2l=12

l=6

Now we can substitute in for s in our simpler equation

s=6-2

s=4

We now know that using our knowledge of systems of equations, the side lengths of this right angle triangle are 6 and 4.