1 Answer

Innochenti · Answer 1 · 2023-11-25T10:39:05+0000

Given:

$(1)/(6)^(\doubleprime)\text{ on a plan for 1 foot }$

The length of the sofa is 6'3''.

We need to convert the foot into inches.

$1\text{ foot = 12 inches.}$
$1^(\prime)=12^(\doubleprime)$

Multiply both sides by 6, we get

$1*6^(\prime)=12*6^(\doubleprime)$

$6^(\prime)=72^(\doubleprime)$

The length of the sofa is

$6^(\prime)3^(\doubleprime)=72^(\doubleprime)+3^(\doubleprime)=75^(\doubleprime)$

The scale of the plan is

$(1)/(6)^(\doubleprime)\colon1^(\prime)$

$(1)/(6)^(\doubleprime)\colon12^(\doubleprime)$

Multiply by 75/12 on both sides, we get

$(75)/(12)*(1)/(6)^(\doubleprime)\colon(75)/(12)*12^(\doubleprime)$

$(75)/(72)^(\doubleprime)\colon75^(\doubleprime)$

$1(3)/(72)^(\doubleprime)=75^(\doubleprime)$

$1(1)/(24)^(\doubleprime)=75^(\doubleprime)$

Hence the length of the sofa on the plan is

$1(1)/(24)^(\doubleprime)$

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