Question 116988
Let W=width, L=length


Since the length is 1 cm longer than it width, this means {{{L=W+1}}}. So if the diagonal is 5 cm, we can find the lengths of the sides given this information



If we cut the rectangle in half along the diagonal, we'll basically have this triangle set up:


{{{drawing(500,500,-0.5,2,-0.5,3.2,

line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,W),
locate(1,-0.2,L),
locate(1,2,5)
)}}}


So we can use Pythagoreans Theorem to find the dimensions


{{{W^2+L^2=5^2}}} 



{{{W^2+(W+1)^2=5^2}}} Plug in {{{L=W+1}}}




{{{W^2+(W+1)^2=25}}} Square 5




{{{W^2+W^2+2W+1=25}}} Foil



{{{W^2+W^2+2W+1-25=0}}} Subtract 25 from both sides



{{{2W^2+2W-24=0}}} Subtract 25 from both sides





{{{2(W+4)(W-3)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{W+4=0}}} or  {{{W-3=0}}} 


{{{W=-4}}} or  {{{W=3}}}    NoW solve for W in each case



So our possible answers are 

 {{{W=-4}}} or  {{{W=3}}} 


However, since a negative width doesn't make sense, our only solution is {{{W=3}}}



Now to find the length, simply add 1 to the width to get


{{{3+1=4}}}


so the width is 3 cm and the length is 4 cm



Check:


{{{W^2+L^2=5^2}}} Start with the given equation




{{{3^2+4^2=5^2}}} Plug in W=3 and L=4



{{{9+16=25}}} Square each term



{{{25=25}}} Add. Since the two sides of the equation are equal, this verifies our answer.