Question

Length, breadth and height of a hall is 150m, 120m and 30m, respectively.find the length of the longest rod that can measure the three dimensions in exact number of times

Answer 1

Answer:

30

Step-by-step explanation:

H.C.F of 150, 120 and 30 is a 30 ,

so the longest rod that measure the room exactly is 30 m rod

I.e 30×1

30×40

30×50

Answer 2

Given: Length, breadth and height of a hall is 150m, 120m and 30m, respectively.

To find: The length of the longest rod that can measure the three dimensions in exact number of times.

Solution:

In order to find the length of the longest rod that can measure the three dimensions in the exact number of times, the length of the diagonal of the hall must be calculated. As evident from the dimensions, the hall is in the shape of a cuboid. Hence, the diagonal of a cuboid can be calculated by using the following formula.

$diagonal = \sqrt{l^{2} +b^{2} +h^{2} }$

Now, the dimensions given in the question are substituted in the formula.

$diagonal = \sqrt{150^{2} + 120^{2} + 30^{2} }$

              $= \sqrt{37,800}$

              $= 194.42 m$

Therefore, the length of the longest rod that can measure the three dimensions in the exact number of times is 194.42.