Answer:
To find the length of the longest rod that can measure the dimensions of the room exactly, we have to find HCF. Length, \[L=8\text{ }m\text{ }50\text{ }cm=850\text{ }cm={{2}^{1}}\times {{5}^{2}}\times 17\] Breadth, \[B=6\text{ }m\text{ }25\text{ }cm=625\text{ }cm={{5}^{4}}\] Height, \[H=4\text{ }m\text{ }75\text{ }cm=475\text{ }cm={{5}^{2}}\times 19\] \[\therefore \] HCF of L, B and His \[{{5}^{2}}=25\text{ }cm\] \[\therefore \] Length of the longest rod \[=25\text{ }cm\]
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