Question 50828
A triange is 1/2 of a rectangle or square, and in this situation, is best defined by its altitude(width = x), base(length = x+1) and hypotenuse(diagonal = 4).  Using the pythagorean theorm...

{{{ a^2 + b^2 = c^2 }}}
{{{ x^2 + (x+1)^2 = 4^2 }}}
F: x * x = x^2
O: x * 1 = 1x
I: 1 * x = 1x
L: 1 * 1 = 1
ADD
{{{ (x+1)^2 = x^2 + 2x + 1 }}}
Substitute
{{{ x^2 + x^2 + 2x + 1 = 4^2 }}}
Combine like terms
{{{ 2x^2 + 2x + 1 = 4^2 }}}
Find 4^2
{{{ 2x^2 + 2x + 1 = 16 }}}
Subtract 16 from both sides
{{{ 2x^2 + 2x -15 = 0 }}}
Can not be factored .... Use the quadratic formula
a=2   b=2   c=-15
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-2 +- sqrt( 2^2-4*2*(-15) ))/(2*2) }}}
{{{x = (-2 +- sqrt( 4-4*2*(-15) ))/(2*2) }}}
{{{x = (-2 +- sqrt( 4-8*(-15) ))/(2*2) }}}
{{{x = (-2 +- sqrt( 4+120 ))/(2*2) }}}
{{{x = (-2 +- sqrt( 124 ))/(2*2) }}}
{{{x = (-2 +- sqrt( 124 ))/(4) }}}
{{{x = (-2 +- sqrt( 124 ))/(4) }}}
{{{x = (-2 +- 11.14)/(4) }}}
From here you can only use the positive root because we are talking about a length.
{{{x = (-2 + 11.14)/(4) }}}
{{{x = (9.14)/(4) }}}
{{{x = (9.14)/(4) }}}
{{{x=2.29}}}
w = 2.29
l = 3.29
Remember, these are estimates.  We rounded the square roots.