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?

Answer 1

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