SOLUTION: 14. Geometry. The perimeter of an isosceles triangle is 37 in. The lengths of the two equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the t

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 14. Geometry. The perimeter of an isosceles triangle is 37 in. The lengths of the two equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the t      Log On


   

Question 123630: 14. Geometry. The perimeter of an isosceles triangle is 37 in. The lengths of the two
equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the
three sides.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of equal leg, y= length of base


Since the perimeter is equal to the sum of all three sides, the perimeter is

P=x%2Bx%2By

which simplifies to

P=2x%2By

Since the " lengths of the two equal legs are 6 in. less than 3 times the length of the base", this means x=3y-6

P=2x%2By Start with the given formula

37=2%283y-6%29%2By Plug in P=37 and x=3y-6

37=6y-12%2By Distribute



37=7y-12 Combine like terms on the right side


0=7y-12-37Subtract 37 from both sides


-7y=-12-37 Subtract 7y from both sides


-7y=-49 Combine like terms on the right side


y=%28-49%29%2F%28-7%29 Divide both sides by -7 to isolate y



y=7 Divide


Since we know that y=7, we can plug this into x=3y-6 to find x


x=3y-6 Start with the given equation

x=3%287%29-6 Plug in y=7

x=21-6 Multiply

x=15 Subtract


So the length of the equal leg is 15 and the length of the base is 7