document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #130451 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
let x = one of the sides
\n" ); document.write( "let y = the base
\n" ); document.write( "---
\n" ); document.write( "base is a whole number that is 4 feet less than the sum of the two sides:
\n" ); document.write( "y = 2x-4
\n" ); document.write( "---
\n" ); document.write( "perimeter of the triangle is a whole number between 0 and 75.
\n" ); document.write( "---
\n" ); document.write( "maximum perimeter is 75.
\n" ); document.write( "equation for maximum perimeter would be:
\n" ); document.write( "2x + y = 75
\n" ); document.write( "since y = 2x-4, this equation becomes:
\n" ); document.write( "2x + 2x - 4 = 75
\n" ); document.write( "which becomes:
\n" ); document.write( "4x - 4 = 75
\n" ); document.write( "add 4 to both sides to get:
\n" ); document.write( "4x = 79
\n" ); document.write( "divide both sides by 4 to get:
\n" ); document.write( "x = 79/4 = 19.75
\n" ); document.write( "---
\n" ); document.write( "if x = 19.75, then substitution in the equation for the base and solve for y:
\n" ); document.write( "y = 2x-4
\n" ); document.write( "y = 2*19.75 - 4
\n" ); document.write( "y = 35.5
\n" ); document.write( "---
\n" ); document.write( "since the base has to be a whole number, 35.5 is no good.
\n" ); document.write( "the nearest integer is either 35 or 36.
\n" ); document.write( "i'll try 35 first.
\n" ); document.write( "---
\n" ); document.write( "y = 35
\n" ); document.write( "y = 2x-4
\n" ); document.write( "solving for x, we get:
\n" ); document.write( "x = (y+4)/2 = 39/2 = 19.5
\n" ); document.write( "---
\n" ); document.write( "perimeter = 2x + y = 39 + 35 = 74
\n" ); document.write( "this is a whole number and is less than or equal to 75 so it should be good.
\n" ); document.write( "----
\n" ); document.write( "let's try 36 next.
\n" ); document.write( "y = 36
\n" ); document.write( "y = 2x-4
\n" ); document.write( "solving for x, we get:
\n" ); document.write( "x = (y+4)/2 = 40/2 = 20
\n" ); document.write( "---
\n" ); document.write( "perimeter = 2x + y = 40 + 36 = 76
\n" ); document.write( "this is a whole number but it is not less than or equal to 75 so it is not good.
\n" ); document.write( "---
\n" ); document.write( "answer appears to be:
\n" ); document.write( "base = 35
\n" ); document.write( "side = 19.5
\n" ); document.write( "maximum perimeter = 74
\n" ); document.write( "---
\n" ); document.write( "the base is a whole number.
\n" ); document.write( "the perimeter is a whole number.
\n" ); document.write( "the base is equal to the sum of the sides plus 4.
\n" ); document.write( "the perimeter is greater than or equal to 0 and less than or equal to 75.
\n" ); document.write( "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.
\n" ); document.write( "the problem does not state that the sides have to be integers so they can contain a fractional part.
\n" ); document.write( "-----
\n" ); document.write( "i believe your answer is:
\n" ); document.write( "base = 35
\n" ); document.write( "sides = 19.5 each
\n" ); document.write( "maximum perimeter = 74
\n" ); document.write( "---
\n" ); document.write( " \n" ); document.write( "
\n" );