Posted by Bethany on Tuesday, February 8, 2011 at 12:47am.
Let the lengths of the legs be a, b and c in increasing order. c is the hypotenuse.
b = a + 5
c = a + 10
c^2 = a^2 + b^2
Three equations in three unknowns. See what you can do with that.
c^2 = a^2 + a^2 + 10a + 25
= 2a^2 + 10a + 25
c^2 = a^2 + 20a + 100
Set the two last equations for c^2 equal to each other and solve for a.
a^2 -10a -75 = 0
(a-15)(a+5) = 0
Only the positive root is allowed.
a = 15
b = 20
c = 25
5
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