w+1=l
area=lw
area=(w+1)w
1500=w²+w
minus 1500 both sides
0=w²+w-1500
use quadratic formula
for
aw²+bw+c=0
\(w= \frac{-b+/- \sqrt{b^2-4ac} }{2a}\)
\(w= \frac{-(1)+/- \sqrt{1^2-4(1)(-1500)} }{2(1)}\)
\(w= \frac{-1+/- \sqrt{1+6000} }{2}\)
\(w= \frac{-1+/- \sqrt{6001} }{2}\)
77.466121627457250675410729387462
\(w= \frac{-1+/- 77.466121627457250675410729387462}{2}\)
it can't be minus since measures cannot be negative
\(w= \frac{-1+ 77.466121627457250675410729387462}{2}\)
\(w= \frac{76.466121627457250675410729387462}{2}\)
w=38.233060813728625337705364693731
to nearest whole
w=38
l=38+1=39
the dimentions are 38 by 39 inches
