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# Maths question. If you have a cuboid of dimensions 5cm, 7cm

Maths question.
If you have a cuboid of dimensions 5cm, 7cm and 12cm can you find the length of the longest diagonal by working out the square root of 52+7+122? Is this a valid short cut and how does it work?

Florian_Berkley :

HelloCustomer no this is not possible. I will explain you why

Florian_Berkley :

Hello, welcome

Florian_Berkley :

I assume you have a rectangular cuboid (=a box like geometry)

Florian_Berkley :

The lenght of the longest diagonal is

Florian_Berkley :

a, b and c are the lenght of the sides (5cm, 7cm and 12cm in your case)

Florian_Berkley :

so the lenght of the longest diagonal in centimeter is D = √(a²+b²+c²) = √(5x5 + 7x7 + 12x12) = √(25 + 49 + 144) = √(218)

Florian_Berkley :

...which is different than calculating the square root of 52 + 7 + 122 = 181

Florian_Berkley :

because √181 ≠ √218

Florian_Berkley :

the lenght of the longest diagonal is D = √(218) = 14,76 cm

Florian_Berkley :

end - please tell me if you need more help :-) Florian