SOLUTION: The lengths of the sides of a plot of land are such that the first leg is 7 miles shorter than the second leg and the hypotenuse is 1 mile longer than the second leg. Find the leng

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The lengths of the sides of a plot of land are such that the first leg is 7 miles shorter than the second leg and the hypotenuse is 1 mile longer than the second leg. Find the leng      Log On


   

Question 946673: The lengths of the sides of a plot of land are such that the first leg is 7 miles shorter than the second leg and the hypotenuse is 1 mile longer than the second leg. Find the lengths of the sides of the plot of land?

I have worked this using Pythagorean theorem and came up with 12, 5, and 13, but I am not sure I did it right. Can anyone confirm my answers for me?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You're right.
We define a variable:
x= length of second .leg.
:x-7= length of second leg;
x%2B1= length of hypotenuse.
We apply the Pythagorean theorem:

cross%28x%5E2%29%2Bx%5E2-14x%2B49=cross%28x%5E2%29%2B2x%2B1
x%5E2-14x%2B49=2x%2B1
<--->%28x-4%29%28x-12%29=0--->system%28x-4=0%2C%22or%22%2Cx-12=0%29--->system%28x=4%2C%22or%22%2Cx=12%29
x=4<--->x-7=4-7<--->x-7=-3 does not work, because it yields a negative number for the length of the first leg.
x=12--->system%28x=12%2Cx-7=12-7%2Cx%2B1=12%2B1%29--->highlight%28system%28x=12%2Cx-7=5%2Cx%2B1=13%29%29%29