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

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) (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

which simplifies to

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

Start with the given formula

Plug in and

Distribute

Combine like terms on the right side

Subtract 37 from both sides

Subtract 7y from both sides

Combine like terms on the right side

Divide both sides by -7 to isolate y

Divide

Since we know that , we can plug this into to find x

Start with the given equation

Plug in

Multiply

Subtract

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

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