How do you find length of a diagonal with height of 2ft, length of 7ft, and width of 10ft?

Question

What formula do you use?

Answer 1

Use the Euclidean distance formula for 3-D space, which is:

L = √[ (x2 - x1)² + (y2 - y1)² + (z2 - z1)² ]

Since we simply have the dimensions here, we can write it in terms of the height, length, and width as follows:

L = √[ (length)² + (width)² + (height)² ]
==> plug in values
L = √[ (7)² + (10)² + (2)² ]
==> simplify exponents
L = √[ 49 + 100 + 4 ]
==> simplify
L = √153 = 3√17 ≈ 12.37 ft ... ANSWER

Answer 2

just use Pythagorean theorem twice. sqrt(10^2+7^2)=12.2.
sqrt(12.2^2+2^2). which equals 12.4

have yourself a good day.