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(1688)   (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
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