# The length, breadth, height of a room are 6.80m, 5.10m, and 3.40m respectively. Find the longest tape which can measure the dimensions of the room exactly?

The longest dimension will be its body diagonal for body diagonal first find the face diagonal

$df = \sqrt {(5.1)^{2} + (6.8)^{2}} \\ df = 8.5 m$

Length of body diagonal

$db = \sqrt {(8.5)^{2} + (3.4)^{2}} \\ db = 9.155 m$

So any tape longer than 9.155 m can measure all the dimensions of the room correctly.

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