Answer:
The length of the diagonal support is 69 feet.
Step-by-step explanation:
Dimensions of the box: length = 6 feet
width = 5 feet
height = 8 feet
The diagonal support relates with the diagonal of the base and the height.
From the base of the box, let the length of its diagonal be represented by x. Applying Pythagoras theorem;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]x^{2}[/tex] = [tex]6^{2}[/tex] + [tex]5^{2}[/tex]
[tex]x^{2}[/tex] = 36 + 25
= 61
x = [tex]\sqrt{61}[/tex]
= 7.81
let the length of the diagonal support be represented by l. So that;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]l^{2}[/tex] = [tex]x^{2}[/tex] + [tex]8^{2}[/tex]
= [tex]\sqrt{61}[/tex] + 64
l = [tex]\sqrt{\sqrt{61} + 64 }[/tex]
= 61 + 8
= 69
Thus, the length of the diagonal support is 69 feet.
