Answer:
[tex]length = l\\width = 5 + l\\Diagonal = 36\\diagonal^2 = (5+l)^2 + l^2\\36^2 = 25 + l^2 +10l + l^2\\1296 = 2l^2 +10l +25 \\2l^2 +10l=1271\\\\l_1=\frac{-10+2\sqrt{2567}}{2\cdot \:2},\:l_2=\frac{-10-2\sqrt{2567}}{2\cdot \:2}[/tex]
[tex]l_1=\frac{-5+\sqrt{2567}}{2},\:l_2=\frac{-5-\sqrt{2567}}{2}[/tex]
clearly,
[tex]l_{2} \ is \ a \ negative\ number[/tex]
So we consider
[tex]l_{1} =\frac{-5+\sqrt{2567}}{2} = 22.83[/tex]
Therefore height = 22.8inches
