Question

The length, breadth and height of a room are 8.25 m, 6.75 m and 4.50 m
respectively. Determine the longest tape which can measure the three dimensions
of the room exactly.​

Answer 1

We have:

Lenght-8.25m

Breath-6.75m

Height-4.50m

We know:

Longest side of a room is daigonal

Formula:

Daigonal of 4 walls is √lenght square+breath square+height square

Explanation:

√l square+b square+h square

√8.25 square+6.75 square+4.50 square

√68.0625+45.5625+20.25

√133.875

11.570436465406

Answer:

Longest tape which can be placed is 11.570436465406

Answer 2

$➪ \sf \red{Answer:-}$

$\huge{ ➫} \tt GIVEN:-$

$length \: of \: room \: = 7m25cm = 725cm \\ breadth \: of \: room \: = 9m25cm = 925cm \\ height \: of \: room \: = 8m25cm = 825cm$

$\huge ➫ \sf FIND:-$

$now \: we \: find \: HCF \: of \: 725,925 \: and \: 825$

${\huge ➫ {\mathfrak{Solution:-}}}$

$725 = 5 \times 5 \times29 \\ 925 = 5 \times 5 \times 37 \\ 825 = 3 \times 5 \times 5 \times 11 \\ \\ so, \: heighest \: common \: factor \: is \: 5 \times 5 = 25 \\ therefore \: HCF \: of \: 725,925,825 \: is \: 25. \\ \therefore 25m is \: the \: longest \: tape \: measure \: which \: can \: measure \: all \: the \: dimensions.$

$so, \: answer \: is \: \boxed{ \mathfrak{ 25m}}$