Question 122761
Use pythagorean theorem
Call the shorter leg {{{x}}}
The longer leg is {{{2x - 3}}}
hypotenuse is {{{18}}} cm
{{{x^2 + (2x - 3)^2 = 18^2}}}
{{{x^2 + 4x^2 - 12x + 9 = 324}}}
{{{5x^2 - 12x - 315 = 0}}}
use quadratic equation to solve
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
When equation is in the form {{{ax^2 + bx + c = 0}}}
{{{a = 5}}}
{{{b = -12}}}
{{{c = -315}}}
{{{x = (-(-12) +- sqrt( (-12)^2-4*5*(-315)))/(2*5) }}}
{{{x = ( 12 +- sqrt( 144 + 6300))/ 10 }}}
{{{x = ( 12 +- sqrt( 6444))/ 10 }}}
{{{x = ( 12 +- 80.275) / 10}}}
{{{x = 92.275 / 10}}}
{{{x = 9.23}}}
check answer
The longer leg is {{{2x - 3}}}
{{{2*9.23 - 3 = 15.46}}}
{{{9.23^2 + 15.46^2 = 18^2}}}
{{{85.19 + 239 = 324}}}
{{{324.19 = 324}}}
obviously, I'm off a little, but you
get the idea