# SOLUTION: An isoscles right triangle has a perimeter of 25 inches, what is the length of the hypotenuse to the nearest ten thousandth? Please help, thank you very much!

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 Click here to see ALL problems on Geometry Word Problems Question 242582: An isoscles right triangle has a perimeter of 25 inches, what is the length of the hypotenuse to the nearest ten thousandth? Please help, thank you very much!Answer by unlockmath(1602)   (Show Source): You can put this solution on YOUR website!Hello, This involves a few steps. First, we know that the two sides of the triangle are the same, so let's represent them with x. We'll let y represent the hypotenuse. We can set up 2 equations which are: x+x+y=25 or rewritten as 2x+y=25 or y=25-2x (And the other equation can be): x^2+x^2=y^2 or rewritten as 2x^2=y^2 With substitution we can do the following: 2x^2= (25-2x)^2 This expands out to: 2x^2=4x^2-100x+625 Subtract 2x^2 from both sides gives us: 0=2x^2-100x+625 Using the Quadratic formula {{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }} plug in the numbers: {{x = (100 +- sqrt( 10000-5000 ))/(2*2) }} turns out to be: x=42.6776 or x=7.3223 (this makes sense so plug it in the original equation) 2(7.3223)+y=25 14.6447+y=25 y=10.3553 This can be checked by adding the sides which are 7.3223 Inches 7.3223 Inches 10.3553 inches which totals approx 25 inches. There you go. I hope this is clear for you. RJ Toftness www.math-unlock.com