Question 996954: Each equal side of an Isosceles 3 1/2 inches longer than the base ,the perimeter of the triangle is 2ft . .Find the length of its base.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is the base.
each side is x + 7/2 inches.
perimeter is 2 feet = 24 inches.
sum of the two sides is 2 * (x + 7/2) inches = 2x + 14/2 inches = 2x + 7 inches.
the sum of the two sides plus the base equals the perimeter.
x is the base and 2x + 7 is the sum of the two sides, so:
the perimeter = x + 2x + 7 = 24
combine like terms to get 3x + 7 = 24.
subtract 7 from both sides to get 3x = 17.
divide both sides by 3 to get x = 17/3 inches.
if x = 17/3 inches, then:
the base is equal to 17/3 inches.
the sum of the two sides is equal to 2 * 17/3 + 7 = 34/3 + 7 = 34/3 + 21/3 = 55/3 inches.
the perimeter is equal to the sum of the base plus the sum of the other two sides which is equal to 17/3 + 55/3 = 72/3 = 24 inches.
since we are already given that the perimeter is equal to 24 inches, then we have just confirmed that x = 17/3 is correct.
you were asked to find the length of the base.
the length of the base = x = 17/3 inches.
you can simplify this further if required to get the base = x = 5 and 2/3 inches.
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