Answer:
2*sqrt(26) is the exact length of AG
10.198 is the approximate length of AG
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Step-by-step explanation:
Draw a line from E to G. Right Triangle EHG has legs EH = 8 and HG = 6. The hypotenuse of triangle EHG is EG = x
Use the pythagorean theorem to find the length of EG
a^2 + b^2 = c^2
8^2 + 6^2 = x^2
64+36 = x^2
100 = x^2
x^2 = 100
x = sqrt(100)
x = 10
EG is 10 units long.
Now focus on triangle AEG. We have AE = 2 as one leg and EG = 10 as the other leg. The hypotenuse is AG = y
a^2 + b^2 = c^2
2^2 + 10^2 = y^2
4 + 100 = y^2
104 = y^2
y^2 = 104
y = sqrt(104)
y = sqrt(4*26)
y = sqrt(4)*sqrt(26)
y = 2*sqrt(26) is the exact length of AG
y = 10.198 is the approximate length of AG
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Shortcut:
You can use the space diagonal formula which is
d = sqrt(L^2 + W^2 + H^2)
In this case, L = 8 is the length, W = 6 is the width and H = 2 is the height. These are the dimensions of the rectangular block. So we then compute d to be...
d = sqrt(L^2 + W^2 + H^2)
d = sqrt(8^2 + 6^2 + 2^2)
d = sqrt(64 + 36 + 4)
d = sqrt(104)
d = sqrt(4*26)
d = sqrt(4)*sqrt(26)
d = 2*sqrt(26) exact length
d = 10.198 approximate length