Posted by Bethany on Tuesday, February 8, 2011 at 12:47am.
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangles be?

Math  drwls, Tuesday, February 8, 2011 at 1:31am
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
(a15)(a+5) = 0
Only the positive root is allowed.
a = 15
b = 20
c = 25
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