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Question 175386: In an isosceles triangle the base is a whole number that is 4 ft less than the sum of the two equal sides. Therefore, the inequality for the base would be x+x-4>0, since the base cannot be 0 or negative. The perimeter of this triangle is a whole number between 0 and 75. Therefore, the equation to find the maximum perimeter would be x+x-4+x+x=75. Find the possible lengths of the equal sides by solving the given inequality for the base and the equation for the perimeter.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let x = one of the sides
let y = the base
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base is a whole number that is 4 feet less than the sum of the two sides:
y = 2x-4
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perimeter of the triangle is a whole number between 0 and 75.
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maximum perimeter is 75.
equation for maximum perimeter would be:
2x + y = 75
since y = 2x-4, this equation becomes:
2x + 2x - 4 = 75
which becomes:
4x - 4 = 75
add 4 to both sides to get:
4x = 79
divide both sides by 4 to get:
x = 79/4 = 19.75
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if x = 19.75, then substitution in the equation for the base and solve for y:
y = 2x-4
y = 2*19.75 - 4
y = 35.5
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since the base has to be a whole number, 35.5 is no good.
the nearest integer is either 35 or 36.
i'll try 35 first.
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y = 35
y = 2x-4
solving for x, we get:
x = (y+4)/2 = 39/2 = 19.5
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perimeter = 2x + y = 39 + 35 = 74
this is a whole number and is less than or equal to 75 so it should be good.
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let's try 36 next.
y = 36
y = 2x-4
solving for x, we get:
x = (y+4)/2 = 40/2 = 20
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perimeter = 2x + y = 40 + 36 = 76
this is a whole number but it is not less than or equal to 75 so it is not good.
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answer appears to be:
base = 35
side = 19.5
maximum perimeter = 74
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the base is a whole number.
the perimeter is a whole number.
the base is equal to the sum of the sides plus 4.
the perimeter is greater than or equal to 0 and less than or equal to 75.
the perimeter cannot be greater than 74 since the base has to be a whole number and going to 36 for the base would result in a perimeter greater than 75 since the sides are in a fixed relationship to the base.
the problem does not state that the sides have to be integers so they can contain a fractional part.
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i believe your answer is:
base = 35
sides = 19.5 each
maximum perimeter = 74
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