Question 1067641
The length and with are the legs of a triangle,
and the diagonal is the hypotenuse.
So {{{w^2 + (2w+44)^2 = (2w+46)^2}}}
subtract {{{(2w+46)^2}}} from each side.
{{{w^2 + (2w+44)^2 - (2w+46)^2= 0}}}
{{{w^2 + 4w^2 + 176w + 1936 - ( 4w^2 + 184w + 2116 ) = 0}}}
{{{w^2 + -8w -180 = 0}}}
factoring,
{{{(w+10)(w-18) = 0}}}
So w = -10 or w = 18
Since we need a positive width, w = 18
The length is 2w+44 = 2(18) + 44 = 36 + 44 = 80
The diagonal is 2w + 46 = 2(18) + 46 = 36 + 46 = 82
Notice that 18^2 + 80^2 = 82^2