Question 24078
length No. 2= 5+x
Length no.1 = x


area of right triangle = {{{1/2 x lw}}}

{{{250 = x(5+x)/2}}}
{{{250 = x^2+5x/2}}}
{{{250(2)=x^2+5x}}}
{{{500=x^2+5x}}}
{{{x^2+5x-500=0}}} 
Use quadratic Forumla:  {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in {{{ax^2+bx+c}}} a= 1, b = 5 and c=-500


{{{x =-5 +- sqrt((5)2-4(1)(-500))/ 2*1)}}}
{{{x=-5+-sqrt(25+2000))/ 2)}}}
{{{x=-5+-sqrt(2025))/ 2)}}}
Add:
{{{x=-5+45/(2)}}}
x=20

20+5=25
And {{{20 x 25/(2)}}}
=250


Hence the one side of the right triangle is 20cm and the other side is 25 cm.
Paul.