Let's start with what we know:
Smaller canvas:
Length ([tex] L_{1} [/tex]) = 3ft
Width ([tex] W_{1} [/tex]) = 5ft
Larger canvas:
Length ([tex] L_{2} [/tex]) = ?
Width ([tex]W_{2} [/tex]) = 10ft
Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:
[tex] \frac{ L_{1} }{ L_{2} } = \frac{ W_{1} }{ W_{2} } [/tex]
So let's plug it all in from above:
[tex] \frac{ 3 }{ L_{2} } = \frac{ 5 }{ 10 } [/tex]
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:
[tex](3)(10) = (5)(L_{2})[/tex]
[tex]30 = 5L_{2}[/tex]
Now divide each side by 5 to isolate [tex]L_{2}[/tex]
[tex] \frac{30}{5} = \frac{ 5L_{2}}{5}[/tex]
The 5s on the right cancel out, leaving us with:
[tex]6 = L_{2} [/tex]
So the length of the larger canvas is 6 ft
