Posted by David Kroell on .
A right triangle has perimeter equal to 80 and hypotenuse equal to 34. What is the area of the triangle?

Geometrey 
Reiny,
let one leg be x
then the other leg is 80  34  x = 46x
x^2 + (46x)^2 = 34^2
x^2 + 2116  92x + x^2 = 1156
2x^2  92x + 960 = 0
x^2  46x + 480 = 0
(x 30)(x16) = 0
x = 30 or x = 16
if x=30, other leg is 4630 = 16
if x = 16 , then other leg is 4616 = 30
(symmetrical solution)
area of triangle = (1/2)(16)(30) = 240 square units 
Geometrey 
David Kroell,
Thanks! :)
I thought it made sense to make it into a quadratic equation.
Stupid me... I didn't factorise correctly.