SOLUTION: I cannot find out how to solve for X when there is two sides with variables and one with a number. I need to solve the pythagorean theorem with the Hypotenus equal to 18, Leg 1 equ

Algebra ->  Pythagorean-theorem -> SOLUTION: I cannot find out how to solve for X when there is two sides with variables and one with a number. I need to solve the pythagorean theorem with the Hypotenus equal to 18, Leg 1 equ      Log On


   

Question 123434This question is from textbook CPM
: I cannot find out how to solve for X when there is two sides with variables and one with a number. I need to solve the pythagorean theorem with the Hypotenus equal to 18, Leg 1 equal to X and Leg 2 equal to 3X. This question is from textbook CPM

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let's just plug the values you have into the Pythagorean Theorem and see what develops

a%5E2%2Bb%5E2=c%5E2

a = x
b = 3x
c = 18
Substitute
x%5E2%2B%283x%29%5E2=18%5E2
Expand
x%5E2%2B9x%5E2=18%5E2
Collect like terms
10x%5E2=18%5E2
Take square root
x%2Asqrt%2810%29=18
Divide by sqrt%2810%29 and rationalize the denominator
x=18%2Fsqrt%2810%29=red%28%2818%2Asqrt%2810%29%29%2F10%29
Giving you the short leg

Multiply result by 3 to get long leg
3x=red%28%2854%2Asqrt%2810%29%29%2F10%29

Check the answer:
sqrt%28%28%2818%2Asqrt%2810%29%29%2F10%29%5E2%2B%28%2854%2Asqrt%2810%29%29%2F10%29%5E2%29
sqrt%28%28324%2A10%29%2F100%2B%282916%2A10%29%2F100%29
sqrt%28324%2F10%2B2916%2F10%29
sqrt%283240%2F10%29
sqrt%28324%29=18 Q.E.D.