SOLUTION: the hypotenuse of a right angled triangle is 20cm. the difference between its other two sides be 4cm. The sides are

Algebra ->  Equations -> SOLUTION: the hypotenuse of a right angled triangle is 20cm. the difference between its other two sides be 4cm. The sides are      Log On


   

Question 896676: the hypotenuse of a right angled triangle is 20cm. the difference between its other two sides be 4cm. The sides are
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
hypotenuse is 20.

one of the sides is x.
the other side is (x+4)

pythagorus says:

x^2 + (x+4)^2 = 20^2 which becomes:

x^2 + x^2 + 8x + 16 = 400

subtract 400 from both sides of the equation and combine like terms to get:

2x^2 + 8x - 384 = 0

divide both sides of the equation by 2 to get:

x^2 + 4x - 192 = 0

factor to get:

(x + 16) * (x - 12) = 0

solve for x to get:

x = -16 or x = 12

x can't be negative so the solution is x = 12

if x = 12, then x+4 = 16

your sides are 12 and 16.

by pythagorus, 12^2 + 16^2 = 20^2 which becomes:

144 + 256 = 400 which becomes:

400 = 400 confirming the solution is good.

the sides are 12 and 16 and the hypotenuse is 20

this triangle is similar to a 3/4/5 triangle since 12/16/20 is a multiple of 3/4/5 by a factor of 4.

the triangles have the same angles and the sides are proportional which is the definition of similar triangles.

you didn't need to know that.

it's an extra.

your solution is that the sides are 12 and 16.