Solution:
Formula of perimeter = [tex] 2(W+H) [/tex]
So, 2W + 2H = 32.4 ... (1)
Ratio = 5:4
So, [tex] \frac{W}{H} =\frac{5}{4} [/tex]
4W - 5H = 0 ... (2)
Solve equation (1) and (2).
W = 9.0 and H = 7.2
Use the Pythagorean theorem,
[tex] W^{2} + H^{2} = D^{2} [/tex]
[tex] D^{2} = (9.0)^{2} + (7.2)^{2} [/tex]
[tex] D^{2} = 132.84 [/tex]
D = 11.52
D = 11.5
Hence, the measure of diagonal is 11.5 inches.
