Question 87998
The diagonal of the rectangle forms the hypoteneuse of a right triangle with the legs of said triangle being the length and the width of the rectangle. Wow, that
was a mouthful. Anyways, they give you that l=w+1. So you can use the pythagorean theorem to write an equation for w:
{{{(w+1)^2+w^2=4^2}}}
Square the binomial and simplify the right hand side:
{{{w^2+2w+1+w^2=16}}}
Put the quadratic in standard form and combine like terms:
{{{2w^2+2w-15=0}}}
Use the quadratic formula:
{{{w=(-2+-sqrt((4-(4*2*(-15)))))/4}}}
Simplify:
{{{w=(-2+-sqrt((4-(-120))))/4}}}
{{{w=(-2+-sqrt(124))/4}}}
You need to have a positive value for the width, so throw away the negative result:
{{{w=(-2+(2)*sqrt(31))/4}}}
Simplify a little more:

{{{highlight(w=(-1+sqrt(31))/2)}}}
You can plug this into your calculator if you need a numerical value.
from the given information, l is just 1+w.
Good Luck,
tutor_paul@yahoo.com