Question

A garage floor measures 150 feet by 120 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit 15 feet. What are the dimensions of the drawing?

Answer 1

10 feet by 8 feet

Explanation:

I choose the following:

Actual width `->W_a=150ft`
Scaled width `->W_s`

Actual length `->L_a =120ft`
Scaled length `->L_s`

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`color(blue)("Consider width - first principles")`

Using ratio in fraction format gives:

`("Actual")/("Scaled") ->15/1-=W_a/W_s=150/W_s`

Turn up the other way (should have done that at the beginning!)

`("Scaled")/("Actual")->1/15-=W_s/150`

`color(green)(1/15color(red)(xx1)-=W_s/150`

`color(green)(1/15color(red)(xx10/10)=W_s/150`

`10/150=W_s/150`

`W_s->" scale width "=10 feet`
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`color(blue)("Consider length")`

`color(brown)("Using short cut method")`

`L_s/L_a->1/15-=L_s/120`

Multiply both sides by 120

`L_s=8 feet`