Question 565570
The hypotenuse of a right triangle is 4 cm long.
 One leg is 1 cm longer than the other. Find the lengths of the legs.
 Round to the nearest tenth.
: 
Let x = one leg 
then
(x+1) = the other leg
:
Remember our good friend pythag, a^2 + b^2 = c^2, so we have
x^2 + (x+1)^2 = 4^2
FOIL (x+1)(x+1)
x^2 + x^2 + 2x + 1 = 16
combine like terms on the left to reveal our old friend, the quadratic equation!
2x^2 + 2x + 1 - 16 = 0
2x^2 + 2x - 15 = 0
Unfortunately this will not factor, use the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation: a=2, b=2, c=-15
{{{x = (-2 +- sqrt(2^2-4*2*-15 ))/(2*2) }}}
:
{{{x = (-2 +- sqrt(4-(-120) ))/4 }}}
:
{{{x = (-2 +- sqrt(124))/4 }}}
the positive solution is all we want here
{{{x = (-2 + 11.1355)/4 }}}
x = {{{9.1355/4}}}
x = 2.28 ~ 2.3 cm, one leg
and
2.3 + 1 = 3.3 cm, the other leg
:
:
Check this on your calc: enter {{{sqrt(2.28^2 + 3.28^2)}}} results 3.99 ~ 4